Sensors and methods for high-sensitivity optical particle counting and sizing

ABSTRACT

A single-particle optical sensor, which has high sensitivity and responds to relatively concentrated suspensions, uses a relatively narrow light beam to illuminate an optical sensing zone nonuniformly. The zone is smaller than the flow channel so that the sensor responds to only a fraction of the total number of particles flowing through the channel, detecting a statistically significant number of particles of any relevant diameter. Because different particle trajectories flow through different parts of the zone illuminated at different intensities, it is necessary to deconvolute the result. Two methods of deconvolution are used: modified matrix inversion or successive subtraction. Both methods use a few basis vectors measured empirically or computed from a theoretical model, and the remaining basis vectors are derived from these few. The sensor is compensated for turbidity. Several embodiments are disclosed employing light-extinction or light-scattering detection, or both.

This is a divisional application of application Ser. No. 10/196,714,filed Jul. 17, 2002.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to methods and apparatus for optical sensing,including counting and sizing of individual particles of varying size ina fluid suspension, and more particularly, to such methods and apparatuswhich yield higher sensitivity and coincidence concentration than can berealized by optical sensors of conventional design.

2. Description of Related Art

It is useful to review the principles underlying the traditional methodof optical particle counting, hereinafter referred to as single-particleoptical sensing (SPOS). Sensors that are used to implement SPOS arebased on the physical technique of light extinction (LE) or lightscattering (LS), or some combination of the two. The optical design of atraditional SPOS sensor based on the LE technique is shown schematicallyin FIG. 1. A fluid, consisting of a gas or liquid, in which particles ofvarious sizes are suspended, is caused to flow through a physical flowchannel 10, typically of rectangular cross section. Two of the opposingparallel surfaces 12 and 14 defining the flow channel are opaque, whilethe remaining two opposing parallel surfaces 16 and 18 perpendicular tothe opaque pair are transparent, comprising the “front” and “back”windows of the flow cell 10. A beam of light 20 of appropriate shapeenters front window 16 of flow cell 10, passes through the flowing fluidand particles, exits flow cell 10 through back window 18 and impinges ona relatively distant light-extinction detector D_(LE).

The width of front and back windows 16 and 18 along the directiondefined by the x-axis is defined as “a” (FIG. 1). The depth of flow cell10, along the direction defined by the y-axis, parallel to the axis ofthe incident light beam, is defined as “b.” Suspended particles ofinterest are caused to pass through flow cell 10 along the directiondefined by the z-axis (from top to bottom in FIG. 1) at a steady,appropriate rate of flow, F, expressed in units of milliliters (ml) persecond, or minute.

The optical sensing zone 22 (“OSZ”), or “view volume,” of the sensor isthe thin region of space defined by the four internal surfaces of flowchannel 10 and the ribbon-like beam of light that traverses channel 10.The resulting shape of the OSZ resembles a thin, approximatelyrectangular slab (having concave upper and lower surfaces, as describedbelow), with a minimum thickness defined as 2w, oriented normal to thelongitudinal axis of flow cell 10 (FIG. 1). Source of illumination 24 istypically a laser diode, having either an elliptical- or circular-shapedbeam, with a gaussian intensity profile along each of two mutuallyorthogonal axes and a maximum intensity at the center of the beam. Twooptical elements are typically required to create the desired shape ofthe incident light beam that, together with the front and back windowsof the flow channel 10, defines the OSZ. The first optical element isusually a lens 26, used to focus the starting collimated beam at thecenter (x-y plane) of flow cell 10. The focused beam “waist,” or width,2w, is proportional to the focal length of the lens and inverselyproportional to the width of the starting collimated beam, defined byits 1/e² intensity values. The focused beam width, 2w, also depends onthe orientation of the beam, if its cross section is not circular.

The second optical element is typically a cylindrical lens 28, used to“defocus,” and thereby widen, the light beam in one direction—i.e. alongthe x-axis. In effect, cylindrical lens 28 converts what otherwise wouldbe a uniformly focused beam (of elliptical or circular cross section)impinging on the flow cell, into a focused “line-source” that intersectsflow channel 10 parallel to the x-axis. The focal length and location ofcylindrical lens 28 are chosen so that the resulting beam width (definedby its 1/e² intensity points) along the x-axis at the center of the flowcell is much larger than the width, a, of the flow channel 10. As aresult, front window 16 of the sensor captures only the top portion ofthe gaussian beam, where the intensity is nearly uniform. Substantialuniformity of the incident intensity across the width (x-axis) of theflow channel 10 is essential in order to achieve optimal sensorresolution. The intensity profile along the z-axis of the resultingribbon-like light beam is also gaussian, being brightest at the centerof the OSZ and falling to 1/e² at its “upper” and “lower” edges/faces,where the distance between these intensity points defines the thickness,2w, of the OSZ.

The shape of the OSZ 22 deviates from that of an idealized, rectangularslab shape suggested in FIG. 1. Rather, the cross-sectional shape of theOSZ in the y-z plane resembles a bow tie, or hourglass, owing to thefact that the incident light beam is focused along the y-axis. However,assuming that the optical design of the sensor has been optimized, thefocal length of the focusing lens will be much larger than the depth, b,of the flow cell. Therefore, the “depth of field” of the focusedbeam—defined as the distance between the two points along the y-axis atwhich the beam thickness expands to {square root}2×2w—will besignificantly larger than the depth, b, of the flow cell. Consequently,the variation in light intensity will be minimal along the y-axis.

The ribbon-like light beam passes through the fluid-particle suspensionand impinges on a suitable light detector D_(LE) (typically a siliconphotodiode). In the absence of a particle in the OSZ, detector D_(LE)receives the maximum illumination. A particle that passes through theOSZ momentarily “blocks” a small fraction of the incident lightimpinging on detector D_(LE), causing a momentary decrease in thephotocurrent output of detector D_(LE) and the corresponding voltage“V_(LE) ” produced by suitable signal-conditioning means. The resultingsignal consists of a negative-going pulse 30 of height ΔV_(LE),superimposed on a d.c. “baseline” level 32 of relatively largemagnitude, V₀, shown schematically in FIG. 2. Obviously, the larger theparticle, the larger the pulse height, ΔV_(LE), both in absolutemagnitude and as a fraction of V₀.

The detector signal, V_(LE), is processed by an electronic circuit 34,which effectively removes the baseline voltage, V₀, typically either bysubtracting a fixed d.c.voltage from V_(LE) or by “a.c. coupling,” usingan appropriate high-pass filter. This action allows for capture of thedesired negative-going pulses of various heights, ΔV_(LE). The resultingsignal pulses are then “conditioned” further, typically includinginversion and amplification. Each pulse is digitized using a fast,high-resolution analog-to-digital (A/D) converter, allowing its heightto be determined with relatively high accuracy. A calibration table isgenerated, using a series of “standard” particles (typically polystyrenelatex spheres) of known diameter, d, spanning the desired size range.This set of discrete values of ΔV_(LE) vs d is stored in computer memoryand typically displayed as log ΔV_(LE) vs log d, with a continuous curveconnecting the points. The set of measured pulse heights, ΔV_(LE), areeasily converted to a set of particle diameters, d, by interpolation ofthe calibration table values.

In principle, there are several physical mechanisms that can contributeto the light extinction effect. These include refraction, reflection,diffraction, scattering and absorbance. The mechanisms of refraction andreflection dominate the LE effect for particles significantly largerthan the wavelength of the incident light, typically 0.6-0.9 micrometers(μm). In the case of refraction, the light rays incident on a particleare deflected toward or away from the axis of the beam, depending onwhether the refractive index of the particle is larger or smaller,respectively, than the refractive index of the surrounding fluid.Provided the two refractive indices differ sufficiently and the (small)detector element, D_(LE), is located sufficiently far from the flowcell, the refracted rays of light will diverge sufficiently that theyfail to impinge on detector D_(LE), thus yielding the desired signal,ΔV_(LE). The mechanism of reflection necessarily accompanies refraction,and the greater the refractive index “contrast” between the particlesand fluid, the greater the fraction of incident light reflected by theparticle. The phenomenon of diffraction typically has a negligibleeffect on the LE signal, because the angles associated with the majorintensity maxima and minima are smaller than the typical solid angledefined by the distant detector D_(LE).

By contrast, however, the light scattering phenomenon typically makes animportant contribution to the LE signal. It is the dominant mechanismfor particles comparable in size to, or smaller than, the wavelength ofthe incident light. The magnitude and angular distribution of thescattered light intensity depends on the size, shape and orientation ofthe particle, as well as the contrast in refractive index and thewavelength of the beam. The well-known Mie and Rayleigh scatteringtheories describe in detail the behavior of the light scatteringintensity. The greater the amount of light scattered off-axis, away fromthe axis of the incident light beam, the smaller the light flux thatreaches the extinction detector D_(LE).

The mechanism of absorbance may be significant for particles that arehighly pigmented, or colored. The magnitude of this effect depends onthe wavelength of the incident light, as well as the size of theparticle. The contribution of absorbance to the overall LE signal may besignificant for particles significantly larger than the wavelength.

There is a simple, approximate relationship between the particle sizeand the magnitude of the LE signal, ΔV_(LE). The total light fluxincident on the detector, D_(LE), in the absence of a particle in theOSZ is proportional to the area of illumination, A₀. This isapproximated byA ₀≈2aw  (1)Assuming that the intensity of the beam incident on the flow channel 10is uniform along both its width, a, and over the thickness, 2w, of thebeam (i.e. assumed to have a rectangular, rather than gaussian,profile).

If one makes the additional simplifying assumption that a particlecompletely blocks the light that impinges on it (i.e. perfect, 100%extinction), then the fraction of incident light blocked by the particleis given by ΔA/A₀, where ΔA represents the cross-sectional area of theparticle. The pulse height, ΔV_(LE), of the light-extinction signal forparticle diameters <2w can then be expressed byΔV _(LE)=(ΔA/A ₀)V ₀  (2)

For simplicity, the particles are assumed to be spherical andhomogeneous, in order to avoid complicating details related to particleshape and orientation. Quantity AA for a particle of diameter d istherefore given byΔA=πd ²/4  (3)

In cases where the particle blocks less than 100% of the light incidenton it—e.g. where the dominant mechanism for extinction is mostly lightscattering, rather than refraction and reflection—quantity ΔA representsthe “effective” cross-sectional area, smaller than the actual physicalarea.

The velocity, v, of the particles that pass through the OSZ is given byv=F/ab  (4)

The pulse width, Δt, represents the time of transit of the particlethrough the OSZ—i.e. between the 1/e² intensity points that define thewidth, 2w. Neglecting the size of the particle compared to quantity 2w,the pulse width is given byΔt=2w/v  (5)

It is instructive to calculate the values of the parameters above for atypical LE sensor—the Model LE400-1E sensor (Particle Sizing Systems,Santa Barbara, Calif.), with a=400 μm, b=1000 μm, and 2w≈35 μm, assumingF=60 ml/min.A ₀=1.4×10⁴ μm²v=250 cm/secΔt=14×10⁻⁶ sec=14 μsecThe smallest particle diameter that typically can be reliably detected(i.e. where ΔVLE exceeds the typical r.m.s. noise level by at least a2:1 ratio) is approximately 1.3 μm. This corresponds to a physicalblockage ratio, ΔA/A₀, of 0.000095, or less than 0.01%.

Increasing the intensity of the light source should, in theory, have noinfluence on the sensitivity, or lower particle size limit, of anextinction-type sensor. For a given baseline voltage, V₀, the pulseheight, ΔV_(LE), depends only on the fraction of the illuminateddetector area effectively blocked by the particle, ΔA/A₀. (The effect ofsample turbidity is discussed later.) Only if a more powerful lightsource possesses lower noise, will the sensor be able to detect reliablya smaller fractional change in effective blocked area, and therefore asmaller particle diameter. However, any such improvement in performance,due to increased S/N ratio, represents only a second-order effect and isusually not significant.

Using the parameters for the LE-type sensor discussed above, one obtainsan estimate of the effective volume, V_(OSZ), of the OSZ,V _(OSZ)=2abw=1.4×10⁷ μm ³=1.4×10⁻⁵ cm ³  (6)The reciprocal of the OSZ volume, 1/V_(OSZ), equals the number of “viewvolumes” contained in 1 cm³ (i.e. 1 ml) of fluid—i.e. 1/V_(OSZ)≈7×10⁴for the example above.

The quantity 1/V_(OSZ) provides a measure of the “coincidence limit” ofthe sensor—the concentration (# particles/ml) at which the particlespass one at a time through the OSZ, provided they are spaced uniformlythroughout the fluid, with each particle effectively occupying one viewvolume at any given time. In reality, of course, the particles arelocated randomly throughout the fluid. Therefore, the particleconcentration must be reduced substantially with respect to this “ideal”value—i.e. by 10:1 or more—in order to ensure the presence of only oneparticle at a time in the OSZ. The actual coincidence limit of thesensor is usually defined as the concentration at which only 1% of theparticle counts are associated with two or more particles passingthrough the OSZ at the same time, possibly giving rise to a singledetected pulse of exaggerated pulse height. Hence, the usefulcoincidence limit of the sensor is typically only 10% (or less) of thevalue 1/V_(OSZ). Using the example above, this implies a coincidenceconcentration of approximately 7,000 particles/ml. In practice thecoincidence limit of a sensor of given design will also be a function ofparticle size. The value indicated is appropriate in the case of veryfine particles, having diameters much smaller than the effectivethickness, 2w, of the OSZ. The coincidence limit may be significantlylower in the case of particles comparable in size to, or larger than,parameter 2w. Therefore, in practice one often chooses to collect dataat a particle concentration of only 50% (or less) of the value givenabove, in order to eliminate erroneous particle “counts” and distortionof the resulting particle size distribution (PSD).

For applications involving concentrated suspensions and dispersions, itis very desirable to increase the coincidence concentration of thesensor, so that less extensive dilution of the starting sample isrequired. First, this improvement lowers the volume of clean fluidneeded to dilute the sample and reduces the extent to which the diluentfluid must be free of particle contamination. Second, and moreimportant, extensive dilution of the starting concentrated suspensionmay not be feasible, if it results in significant changes in thePSD—e.g. due to promotion of particle agglomeration. Examples includepH-sensitive oxide “slurries” used for processing semiconductor wafersby the method known as chemical mechanical planarization (CMP). Also,for a variety of applications it is useful, if not essential, toincrease the sensitivity of the SPOS method—i.e. to reduce the minimumdetectable particle size. Increases in the coincidence concentration andimprovements in the sensitivity of LE-type sensors are usually related,and there are several ways in which improvements in both parameters canbe achieved.

The most obvious way in which the sensitivity of an extinction-typesensor can be improved is to decrease the cross-sectional area ofillumination, A₀. Using the example above, this is accomplished bydecreasing the lateral cell dimension, a, or the incident beamthickness, 2w, or both. Concerning the latter course of action, theeffective thickness, 2w, of the OSZ can be reduced only to a limitedextent. This limitation is imposed by the relationship between the focallength of the focusing lens, the depth of the flow cell, and the widthof the starting light beam. Given the nature of gaussian beam optics andthe limitations imposed by diffraction, it is impractical to decreaseparameter 2w below approximately 5 μm. This reduction represents only a7-fold improvement over the 35-μm value assumed in the example above.Furthermore, in order to achieve relatively high size resolution forsmaller particles, it is useful to retain the quadratic dependence ofthe light-extinction pulse height, ΔV_(LE), on the particle diameter, d,which obtains only for values of d (substantially) smaller than 2w.Hence, in order to achieve optimal performance for many importantapplications, it is usually not desirable to make the thickness of theOSZ appreciably thinner than about 10 μm.

Instead, it appears to be more attractive to reduce the lateraldimension, a, of the OSZ—e.g. from 400 μm (using the example above) to40 μm. To a first approximation (ignoring nonlinear signal/noiseeffects), this 10-fold reduction in A₀ results in a similar 10-foldreduction in the effective cross-sectional area, ΔA_(LE), required toachieve a given fraction of blocked area, ΔA_(LE)/A₀.

There is a second significant advantage that results from this 10-foldreduction of the width of the flow channel 10. The volume of the OSZ(Equation 6) is also reduced 10-fold, resulting in a reduction of thecoincidence concentration by the same factor. Hence, the working sampleconcentration can be increased 10-fold, permitting a 10-fold lowerextent of dilution required for the starting concentrated particledispersion. Of course, the same 10-fold increase in the coincidenceconcentration can be achieved through a 10-fold reduction in the celldepth, b, rather than the cell width, a, considered above. However, theimprovement in sensor sensitivity would no longer be obtained. Clearly,while dimensions “a” and “b” play equivalent roles with respect todetermining V_(OSZ), and therefore the coincidence concentration, theyare not equivalent with respect to influencing sensor sensitivity.

Unfortunately, there is a serious disadvantage to this proposedapproach. It is not practical to reduce dimension a (or b, for thatmatter) to such an extent (i.e. significantly smaller than 100 μm) forreasons that are obvious to anyone familiar with the use of SPOStechnology. Such a small dimension virtually invites clogging of theflow channel 10, due to the inevitable existence of contaminant (“dirt”)particles in the diluent fluid and/or large particles associated withthe sample, such as over-size “outliers” and agglomerates of smaller“primary” particles. Generally, the minimum lateral dimension (either aor b) of the flow channel 10 in an LE-type sensor should be at leasttwo, and preferably three to four, times larger than the largestparticle expected to occur in the sample of interest. Otherwise,frequent clogging of the flow cell is inevitable, thus negating one ofthe principal advantages of the SPOS technique over an alternativesingle-particle sensing technique known as “electro-zone,” or“resistive-pore,” sensing (e.g. the “Coulter counter,” manufactured byBeckman-Coulter Inc, Hialeah, Fla.).

One of the previously established ways of increasing the sensitivity ofa conventional SPOS-type sensor is to use the method of light scattering(LS), rather than light extinction. With the LS technique thebackground, or baseline, signal is ideally zero in the absence of aparticle in the OSZ. (In reality, there is always some low-level noisedue to scattering from contaminants and solvent molecules, pluscontributions from the light source, detector and amplifier.) Therefore,the height of the detected signal pulse due to a particle passingthrough the OSZ can be increased, for a given particle size andcomposition, simply by increasing the intensity of the light source.This simple expedient has resulted in sensors that can detect individualparticles as small as 0.2 μm or smaller.

Fortunately, by adopting a completely different measurement approach,significantly higher sensitivity and coincidence concentration can beachieved from an SPOS device than is provided by a conventional LE or LSsensor. The resulting new apparatus and method form the basis of thepresent invention. The most significant difference in the optical designof the new sensor concerns the light beam that is used to define theOSZ. Rather than resembling a thin “ribbon” of light that extends acrossthe entire flow channel (i.e. in the x-y plane, FIG. 1), it now consistsof a thin “pencil” of light (aligned with the y-axis) that probes anarrow region of the flow channel 10. This beam, typically having anapproximately gaussian intensity profile and circular cross section,effectively illuminates only a small fraction of the particles that flowthrough the sensor. The resulting area of illumination, A₀, is muchsmaller than the value typically found in a conventional sensor, whichrequires that the beam span the entire width (x-axis) of the flowchannel 10. By definition, the intensity of the new beam is highlynon-uniform in both the lateral (x-axis) direction and the direction ofparticle flow (z-axis).

Consequently, particles that pass through the sensor are necessarilyexposed to different levels of maximum light intensity (i.e. at z=0),depending on their trajectories. The resulting signal pulse heightgenerated by a particle now depends not only on its size, but also itspath through the flow channel 10. Particles that pass through the centerof the illuminating beam, where the intensity is highest, will generateLE (or LS) pulses of maximum height for a given size, while those thatpass through regions of lesser intensity will produce pulses ofcorresponding reduced height. Hence, the use of a beam of non-uniform(usually, but not necessarily gaussian) intensity profile gives rise tothe so-called “trajectory ambiguity” problem. A number of researchershave attempted to address this problem, using a variety of approaches.

The problem of trajectory ambiguity in the case of remote in-situmeasurement of scattered light signals produced by unconfined particleswas discussed more than twenty years ago by D. J. Holve and S. A. Self,in Applied Optics, Vol. 18, No. 10, pp. 1632-1652 (1979), and by D. J.Holve, in J. Energy, Vol. 4, No. 4, pp. 176-183 (1980). A mathematicaldeconvolution scheme, based on a non-negative least-squares (NNLS)procedure, was used to “invert” the set of measured light scatteringpulse heights produced by combustion particles moving in free space. Themeasurement volume was defined by a ribbon (elliptical) beam with agaussian intensity profile and an off-axis distant pinhole and detector,reverse imaged onto the beam. Holve et al explicitly rejected thewell-known method of matrix inversion, as it was said to be ineffectivewhen applied to their typical light scattering data. From the resultsand explanation provided, it is apparent that the resolution andaccuracy of the PSDs that could be obtained using their light scatteringscheme and NNLS deconvolution procedure were relatively poor. Multimodaldistributions required relatively widely spaced particle sizepopulations in order to be resolved reasonably “cleanly” using thereferenced apparatus and method.

As disclosed in the Holve articles, the measurement region from whichthe scattered light signal is detected originates from a portion of thecross section of the illuminating beam. As will be discussed, thepresent invention also utilizes a beam that is spatially non-uniform inintensity, preferable having a circular gaussian profile. However, thepresent invention fully “embraces” this non-uniformity. That is, themeasurement zone encompasses the entire cross section of the beam andnot just the central region of highest (and least-variable) intensity.The particles to be counted and sized are caused to flow uniformlythrough a confined, well-defined space (flow channel) where the fractionof particles of any given size that is measured is fixed and ultimatelyknown. The region from which data are collected is similarly fixed andwell-defined and relatively immune to vibrations and opticalmisalignment. Given the inherent stability and different nature of thephysical design associated with the present invention, it should not besurprising that the PSD results possess not only high sensitivity butalso superior, unprecedented particle size resolution compared to theresults obtained from the Holve approach. It is observed also thatHolve's system is necessarily confined to light scattering as the meansof detection. By contrast, the novel apparatus and methods taught in thepresent invention make possible sensors that are equally effective basedon light scattering or light extinction.

Partly because of the limited quality of the PSD results that could beachieved using the apparatus and method described by Holve et al, therewas subsequent recognition of the need to develop alternative methodsthat would permit gaussian beams to be used effectively for particlesize determination. Of course, the simplest remedy, if appropriate, wasseen to be elimination of the gaussian beam, itself, that is the sourceof the problem. Foxyag, in U.S. Pat No. 3,851,169 (1974), proposedaltering the intensity distribution of the laser beam, in order toreduce the non- uniformity inherent in its gaussian profile. Separately,G. Grehan and G. Gouesbet, in Appl. Optics, Vol 25, No. 19, pp 3527-3537(1986), described the use of an “anti-gaussian” correcting filter in anexpanded beam before focusing, thereby producing a “top-hat” beamprofile, having substantially uniform intensity over an extended region.Fujimori et al, in U.S. Pat. No. 5,316,983 (1994), used a “soft” filterto convert a gaussian laser beam into a flattened intensitydistribution.

Other proposals involved physically confining the flowing particles, sothat they are forced to pass through the central portion of the laserbeam, where the intensity is substantially uniform. An example isdescribed by J. Heyder, in J. Aerosol Science, Vol 2, p. 341 (1971).This approach was also adopted by Bowen, et al, in U.S. Pat. No.4,850,707 (1989), using a focused elliptical laser beam with a gaussianintensity profile, with a major axis much longer than the width of ahydrodynamically-focused “channel” containing the flowing particles. Allof the particles are therefore exposed to substantially the same maximumintensity as they flow through the beam.

An early proposal for accommodating gaussian beams, proposed byHodkinson, in Appl. Optics, Vol. 5, p. 839 (1966), and by Gravitt, inU.S. Pat. No. 3,835,315 (1974), was to determine the ratio of the peakscattered intensity signals detected simultaneously at two differentscattering angles. This ratio is ideally independent of the intensityincident on the particle and, according to Mie theory, is uniquelyrelated to its size. The reliability of this method was improved usingthe proposal of Hirleman, Jr., et al, in U.S. Pat. No. 4,188,121 (1980).The peak scattered intensities at more than two scattering angles aremeasured and the ratios of all pairs of values calculated. These ratiosare compared with calibration curves in order to establish the particlediameter.

Several methods were suggested for selecting only those particles thathave passed substantially through the center of the gaussian beam. Ascheme for collecting off-axis scattered light from a distant, in-situmeasurement volume, similar to the apparatus used by Holve et al, wasdescribed by J. R. Fincke, et al, in J. Phys. E: Sci. Instrum., Vol 21,pp. 367-370 (1988). A beam splitter is used to distribute the scatteredlight between two detectors, each having its own pinhole aperture. Oneof the apertures is smaller than the beam waist in the measurementvolume. Its detector is used to “select” particles suitable formeasurement by the second detector, having a considerably largeraperture, ensuring that they pass substantially through the center ofthe beam, and therefore are eligible for counting and sizing.Notwithstanding the simplicity and apparent attractiveness of thisapproach, it was ultimately rejected by the authors, because of thedifficulty of maintaining precise, stable alignment of the variousoptical elements. (This rejection is not unrelated to the limitedquality of the PSD results obtained by Holve et al, alluded to above.)

Another set of proposed methods suggested the use of two concentriclaser beams of different diameters, focused to a common region, throughwhich particles are allowed to transversely flow, with the outside beamsignificantly larger in diameter than the inner beam. Two detectors areused to measure the amplitudes of light signals scattered by particlespassing through each respective beam, distinguished by differentwavelength (color) or polarization. Only those particles that passthrough the central portion of the larger measurement beam, where theintensity is substantially uniform, produce signals from the smaller“validating” beam. Schemes using beams of two different colors aredescribed by Goulas, et al, in U.S. Pat. No. 4,348,111 (1982), andAdrian, in U.S. Pat. No. 4,387,993 (1983). A variation on the concentrictwo-beam method is described by Bachalo, in U.S. Pat. No. 4,854,705(1989). A mathematical formulation is used to process the twoindependently measured signal amplitudes together with the known beamdiameters and intensities to determine the particle trajectory and,ultimately, the particle size. A variation on this approach is describedby Knollenberg, in U.S. Pat. No. 4,636,075 (1987), using two focused,concentric beams distinguished by polarization. An elongated, ellipticalbeam shape is used to reduce the ratio of beam diameters needed toachieve acceptable particle size resolution and higher concentrationlimits.

Yet another variation of the two-beam approach is described byFlinsenberg, et al, in U.S. Pat. No. 4,444,500 (1984). A broad“measuring” beam and a narrower “validating” beam are again utilized,but in this case the latter is located outside the former, allowing bothbeams to have the same color and polarization. The plane containing theaxes of the two beams is aligned parallel to the flow velocity of theparticles. Achieving coincidence of two scattering signals detectedseparately from each beam ensures that the only particles to be countedand sized are those that have traversed the narrow beam, and hence thecentral region of the broad, measuring beam. Still another variation ofthe two-beam approach is described by Hirleman, Jr., in U.S. Pat. No.4,251,733 (1981). Through the use of two physically separated gaussianbeams, the particle trajectory can be determined from the relativemagnitudes of the two scattered light signal pulses. This, in turn,permits the intensity incident on the particle everywhere along itstrajectory to be calculated, from which the particle size can bedetermined.

Other proposals take advantage of an interferometric technique commonlyutilized in laser Doppler velocimetry—i.e. crossing two coherent laserbeams to obtain a fixed fringe pattern in a spatially localized region.The particle size can be determined from the peak scattering intensity,provided differences in trajectory can be accounted or compensated for.A straightforward scheme was proposed by Erdmann, et al, in U.S. Pat.No. 4,179,218 (1979), recognizing that a series of scattered lightpulses is produced by each particle, related to the number of fringesthrough which it passes. The number of pulses establishes how close theparticle has approached the center of the “probe” volume established bythe fringe pattern, where the number of fringes is greatest and theintensity is brightest, corresponding to the center of each gaussianbeam. An alternative method was proposed by C. F. Hess, in Appl. Optics,Vol. 23, No. 23, pp. 4375-4382 (1984), and in U.S. Pat. No. 4,537,507(1985). In one embodiment, two coherent beams of unequal size arecrossed, forming a fringe pattern. The small beam “identifies” thecentral region of the larger beam, having substantially uniform(maximal) intensity. A signal that contains the maximum a.c. modulationindicates that the particle has passed through the center of the fringepattern and, hence, the middle of the large beam. The particle size isextracted from the “pedestal” (d.c.) signal after low-pass filteringremoves the a.c. component. In a second embodiment, two crossed laserbeams of one color are used to establish a fringe pattern at the centerof a third, larger beam of a second color. A first detector establishesfrom the magnitude of the a.c. component of the scattered light signalwhether a particle has passed substantially through the center of thefringe pattern. If so, the pulse height of the scattered light producedby the large beam, obtained from a second detector, is recorded.Bachalo, in U.S. Pat. No. 4,329,054 (1982), proposed distinguishing thecentral portion of a fringe pattern, corresponding to the central regionof each gaussian beam, by using an additional small “pointer” beam ofdifferent color or polarization, responding to a separate detectormeans.

Finally, assorted other techniques have been proposed for addressing thegaussian beam/trajectory ambiguity problem. Bonin, et al, in U.S. Pat.No. 5,943,130 (1999), described a method for rapidly scanning a focusedlaser beam through a measurement volume, resulting in a scatteredintensity pulse each time the beam crosses a particle. Given the highscanning frequency and velocity and the relatively low particlevelocity, each particle is scanned several times while it is in themeasurement volume. The resulting series of pulses can be fitted to thebeam intensity profile and the maximum of the gaussian fit mapped to aparticle diameter using a calibrated response function that correlatesparticle size with scattered light intensity. DeFreez, et al, in U.S.Pat. No. 6,111,642 (2000), proposed a “flow aperturing” technique. Aparticle/fluid delivery nozzle is designed so that the lateral velocityprofile of the emerging particles approximately matches the gaussianintensity profile of the laser beam. The reduction in incident lightlevel due to increasing distance of the particle trajectory from thebeam axis is compensated approximately by the increase in integrationtime of the scattering signal, due to the lower velocity. The netintegrated scattering signal is therefore ideally independent of thetrajectory. An improvement was proposed by Girvin, et al, in U.S. Pat.No. 6,016,194 (2000), using a linear detector array to individuallydetect the scattered light signals associated with substantially eachparticle trajectory. The gain of each detector element can be adjustedto compensate for variations that remain in the net signal response ofthe system in the lateral direction, due to incomplete matching of thenozzle velocity and laser beam intensity profiles, differences inindividual detector efficiencies and other effects.

SUMMARY OF THE INVENTION

It is the object of the invention to provide an SPOS device and methodwhich provide significantly higher sensitivity and the ability torespond effectively to fluid suspensions which are relativelyconcentrated with a higher concentration of particles than is usual inthe art and which, therefore, need not be diluted to the same degree asis required with prior art SPOS devices.

An SPOS device according to the invention establishes flow of thesuspension through a physically well-defined measurement flow channel. Arelatively narrow beam of light is directed through the measurement flowchannel to illuminate an optical sensing zone within the measurementflow channel, the beam of light and the optical sensing zone being ofsuch size relative to the size of the measurement flow channel that theSPOS device responds to a small fraction of the total number ofparticles flowing through the measurement flow channel with the resultthat the SPOS device will respond effectively to a relativelyconcentrated fluid suspension. The beam illuminates the optical sensingzone non-uniformly, having a central maximum intensity portion and acontinuum of lesser intensities for positions spaced from the maximumintensity portion, so that some of the particles have trajectoriesthrough the maximum intensity portion, others of the particles havetrajectories through the lesser intensity portions, and still others ofthe particles may have trajectories outside the zone.

The measurement flow channel has a thickness dimension axially of thebeam of light, a width, or lateral, dimension transverse to the beam anda flow direction perpendicular to the thickness and width dimensions.The beam, which is much narrower than the measurement flow channel inthe width direction, may be focused with a depth of field which issubstantially larger than the thickness dimension, so that the beam hasan effective width which does not vary substantially over the thicknessdimension. The effective width which is defined as the width betweenopposing positions in the beam at which said lesser intensities havefallen to a given fraction, such as 1/e², of said maximum intensity, ischosen so that particles can be effectively sized over the range ofparticles to be sized and is typically substantially one half the sizeof the largest particle to be sized. The intensity of the beam is highlynon-uniform in the lateral direction and the direction of particle flowand may have a gaussian intensity profile. The beam may be circular incross-section or elliptical, being wider transverse to the beam in thedirection perpendicular to particle flow than in the direction parallelto particle flow.

The SPOS device of the invention uses a photo-detector and may operateon a light-extinction or light-scattering principle. Indeed, some sensorembodiments include both detection techniques. The photo-detectordetects light from the zone to provide pulse height signals, eachresponsive to a particle flowing through said zone, the pulse heightsignals being functions of the sizes and trajectories of detectedparticles, particles of a given size providing a maximum pulse heightsignal when flowing through the maximum intensity portion and lesserpulse height signals when flowing through the lesser intensity positionsof the zone. The pulse height signals, collectively, form a pulse heightdistribution (PHD). A statistically significant number of particles ofthe given size flow through the lesser intensity positions of the zone.

The use of a non-uniform beam creates the “trajectory ambiguity”problem. For this reason, the device and method include means formathematically deconvoluting the pulse height distribution to provide aparticle size distribution of the particles in the suspension. Accordingto the invention, the deconvolution method is an improvement overdeconvolution as taught in the prior art. The invention proposes the useof two deconvolution techniques: one using matrix inversion, and theother using successive subtraction.

Both techniques use a matrix. According to this invention, the processof setting up the matrix is simplified. The matrix has column basisvectors, each corresponding to a particular particle size. It has beenproposed in the prior art to empirically base the values of all of thecolumn basis vectors on measurements of particles of uniform, knownsize. Since the matrix may have a large number of columns (32, 64 and128 are proposed in this application), according to the presentinvention only one or a few of the column basis vectors, oralternatively, none of them, need be empirically based on measurementsof particles of known size. The remaining column basis vectors arecomputed by interpolation and/or extrapolation from empirically basedcolumn basis vectors. It is also proposed by this invention that some,or all, of the column basis vectors can be computed from a theoreticalmodel. If some of them are so computed, the remaining column basisvectors can be computed by interpolation and/or extrapolation from thosecomputed from existing data.

It is proposed to modify a method of deconvolution by matrix inversion.Each column basis vector has a maximum count pulse height at a locationfor a row which relates to a pulse height channel corresponding to aparticle of known size associated with the column basis vector, themaximum count pulse height values for successive columns being arrangedin a diagonal of the matrix. The matrix is modified by setting all termsbelow the diagonal to zero—that is to say, all terms corresponding topulse height values greater than the maximum count pulse height value ina column are set to zero. This improves the accuracy, signal/noise ratioand reproducibility of the result.

The proposed method of deconvolution by successive subtraction involvessetting up a matrix having a plurality of columns each containing abasis vector comprising a pulse height distribution of particles of aknown size, each successive column containing a basis vector forparticles of successively larger sizes, and a maximum-size basis vectorcontaining a pulse height distribution for maximum size particles. Thesuccessive subtraction algorithm comprises the steps of:

-   -   starting with the basis vector with its maximum count value in        the row corresponding to the largest pulse height;    -   scaling a column basis vector by a factor corresponding to the        value of the row in the PHD that matches the column number;        subtracting said scaled basis vector from the PHD to form an        element of the deconvoluted PHD (dPHD), leaving an intermediate        PHD vector with a smaller total number of particles;    -   and repeating this process using the remaining basis vectors        until the entire PHD has been substantially consumed and all the        elements of deconvoluted DPHD have been formed.

Using a calibration curve of the relationship of pulse height anddiameter, each deconvoluted pulse height value in the dPHD is translatedinto a unique particle diameter associated with this pulse height valueyielding a raw particle size distribution, PSD. The raw PSD is convertedinto a final PSD by normalizing the raw PSD by multiplying it by thevalue 1/φ_(d), where φ_(d) is the fraction of particles actuallydetected by said device for particles of each size, d.

When the fluid suspension is relatively concentrated, light extinctiontype sensors may be affected by turbidity. Compensation for turbiditymay be provided in one of three ways. First the baseline voltage levelsfor turbid and non-turbid liquids are sensed, a ratio is computed, andthis ratio is used to increase the amplitude of the light-extinctionsignal such that the baseline voltage level for the turbid liquid isincreased to approximately the baseline voltage level for the non-turbidliquid. Second, the pulse height signals generated by the turbid liquidare corrected by the computed ratio. Third, the intensity of thestarting beam of light is adjusted in response to the ratio tocompensate for turbidity.

An embodiment of the invention includes both a light-extinction (LE)detector and a light-scattering (LS) detector. Scattered light from thezone is passed to the (LS) detector through a mask to select lightscattered between a first and a second angle to the beam. Lighttransmitted through the zone is directed to the LE detector. Anotherembodiment uses an optical fiber for conveying light from a light sourceto the optical sensing zone and projecting said light through the zoneand an optical fiber for conveying the light from the zone to a LEdetector. Scattered light from the zone is passed through a mask toselect light scattered between a first and a second angle to the beamand this scattered light is collected by the LS detector. A furtherembodiment comprises a light source, a beam splitter for providing twolight beams directed through a pair of optical sensing zones positionedwithin the measuring flow channel, each beam having an effective widthcompatible with a different range of particle sizes. Another embodimentcomprises a light-scattering detector and means for passing a portion ofthe light through one of a plurality of masks located on a rotatablewheel, and means for selecting one of these masks by rotating the wheelto a desired orientation, each mask defining different angles betweenwhich the light is scattered and collected. A final embodiment projectsa relatively wide collimated beam through the optical sensing zone. Thebeam has a central axis, and an acceptance aperture captures only thoselight rays that closely surround the central axis of the beam. Thisreduces the effective width of the beam to a width in a directiontransverse to the axis of the light beam that is substantially one-halfthe size of the largest particle to be sized. An optical fiber couplesthe light rays to a detector.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other objects, features and advantages of the invention willbe more fully appreciated with reference to the accompanying Figures, inwhich:

FIG. 1 is a simplified block diagram of the optical scheme typicallyused in a conventional prior art LE sensor;

FIG. 2 is a simplified representation of the time-dependent outputsignal voltage generated by the conventional LE sensor of FIG. 1;

FIG. 3 is a simplified block diagram of the LE-type sensor of thepresent invention, hereinafter the “new LE-type sensor,” using arelatively narrow, focused light beam to illuminate particles flowing ina relatively thin flow channel;

FIG. 4 shows a typical pulse height distribution (PHD) obtained from theLE-type sensor of FIG. 3, using uniform polystyrene latex (standard)particles of diameter 1.588-μm;

FIG. 5 is a schematic diagram showing the relationship between particletrajectory and the resulting PHD, for an incident light beam with anon-uniform, gaussian intensity profile;

FIG. 6 compares the PHDs obtained for 1.588-μm and 2.013-μm polystyrenelatex (standard) particles using the new LE-type sensor;

FIG. 7 compares the PHDs obtained using the new LE-type sensor foruniform polystyrene latex (standard) particles of eight different sizes:0.806-μm, 0.993-μm, 1.361-μm, 1.588-μm, 2.013-μm, 5.03-μm, 10.15-μm and20.0-μm;

FIG. 8A shows the maximum measured pulse height versus particle diameterfor the eight polystyrene latex (standard) particle suspensionsdisplayed in FIG. 7;

FIG. 8B compares theoretical predictions (perfect extinction, gaussianbeam) with experimental results (FIG. 8A, solid circles) for the maximumpulse height (expressed as a percentage of 100% extinction) versesparticle diameter, theoretical curves being shown for beam widths (1/e²)of 10-μm (open squares), 11-μm (open circles) and 12-μm (opentriangles);

FIG. 9 shows the dependence of the measured sensor efficiency, φ_(d), asa function of particle diameter, d, over the range 0.806- to 20.0-μm;

FIG. 10 shows the theoretical predictions (perfect extinction, gaussianbeam) for the maximum pulse height (expressed as a percentage of 100%extinction) versus particle diameter for various beam widths: 6-μm (opencircles), 9-μm (open squares), 12-μm (open triangles), 15-μm (closedcircles), 18-μm (closed squares) and 21-μm (closed triangles);

FIG. 11 is a simplified block diagram of the LS-type sensor of thisinvention, hereinafter the “new LS-type sensor,” using a relativelynarrow, focused light beam to illuminate particles flowing in arelatively thin flow channel;

FIG. 12 is a simplified representation of the time-dependent outputsignal voltage generated by the new LS-type sensor;

FIG. 13A and FIG. 13B contain flow diagrams for two mathematicalalgorithms (matrix inversion and successive subtraction, respectively)that can be used to deconvolute the measured PHD data;

FIG. 14 is a flow chart summarizing the operation and structure of thenew LE- and LS-type sensors, including the measurement and computationalsteps needed to obtain the PSD;

FIG. 15A shows the measured PHD (64-channel resolution) obtained fromsample “A” (latex trimodal, 0.993-, 1.361- and 1.588-μm) using the newLE-type sensor;

FIG. 15B shows the measured PHD obtained from sample “B” (same as Sample“A,” but only 50% of the 0.993-μm latex) using the new LE-type sensor;

FIG. 15C shows the measured PHD obtained from sample “C” same as Sample“A,” but only 25% of the 0.993-μm latex) using the new LE-type sensor;

FIG. 16A and FIG. 16B show a representative 32×32 matrix used fordeconvolution of measured PHDs, obtained from nine measured basisvectors that span a size range from 0.722- to 20.0-μm;

FIG. 17 shows the measured PHD vectors (32×1) obtained from the trimodalsamples “A,” “B” and “C” (same as FIGS. 15A, 15B, 15C, but with32-channel resolution) and the resulting dPHD vectors obtained bydeconvolution using the matrix of FIGS. 16A and 16B of the threemeasured PHD vectors, using both matrix inversion and successivesubtraction;

FIG. 18A shows the computed dPHD (64-channels) obtained from themeasured PHD for sample “A” (latex trimodal, FIG. 15A), using the matrixinversion algorithm;

FIG. 18B shows the computed DPHD obtained from the measured PHD forsample “B” (latex trimodal, FIG. 15B), using the matrix inversionalgorithm;

FIG. 18C shows the computed dPHD obtained from the measured PHD forsample “C” (latex trimodal, FIG. 15C), using the matrix inversionalgorithm;

FIG. 19A shows the computed dPHD (64-channels) obtained from themeasured PHD for sample “A” (latex trimodal, FIG. 15A), using thesuccessive subtraction algorithm;

FIG. 19B shows the computed dPHD obtained from the measured PHD forsample “B” (latex trimodal, FIG. 15B), using the successive subtractionalgorithm;

FIG. 19C shows the computed dPHD obtained from the measured PHD forsample “C” (latex trimodal, FIG. 15C), using the successive subtractionalgorithm;

FIG. 20A shows the PSD (concentration) obtained for sample “A” from thecomputed dPHD (FIG. 19A), using the calibration curve (FIG. 8A) andsensor efficiency (FIG. 9);

FIG. 20B shows the PSD (concentration) obtained for sample “B” from thecomputed dPHD (FIG. 19B), using the calibration curve (FIG. 8A) andsensor efficiency (FIG. 9);

FIG. 20C shows the PSD (concentration) obtained for sample “C” from thecomputed dPHD (FIG. 19C), using the calibration curve (FIG. 8A) andsensor efficiency (FIG. 9);

FIG. 21A shows the measured PHD (32-channels) obtained for a sample offat emulsion (0.05% by volume);

FIG. 21B shows the measured PHD obtained for the same sample as used inFIG. 21A, but with an added, low-concentration “spike” of 0.993-μm latexparticles (3.25×10⁵/ml);

FIG. 21C shows the measured PHD obtained for the same sample as used inFIG. 21B, but with only 25% of the added “spike” of 0.993-μm latexparticles (8.13×10⁴/ml);

FIG. 22A shows the computed dPHD (valid pulse-ht region) obtained bydeconvolution (successive subtraction) of the PHD in FIG. 21A;

FIG. 22B shows the computed dPHD (valid pulse-ht region) obtained bydeconvolution (successive subtraction) of the PHD in FIG. 21B;

FIG. 22C shows the computed dPHD (valid pulse-ht region) obtained bydeconvolution (successive subtraction) of the PHD in FIG. 21C;

FIG. 23A shows the PSD (concentration, expanded scale) obtained from thecomputed dPHD (FIG. 22A), using the calibration curve (FIG. 8A) andsensor efficiency (FIG. 9);

FIG. 23B shows the PSD (concentration, expanded scale) obtained from thecomputed DPHD (FIG. 22B), using the calibration curve (FIG. 8A) andsensor efficiency (FIG. 9);

FIG. 23C shows the PSD (concentration, expanded scale) obtained from thecomputed dPHD (FIG. 22C), using the calibration curve (FIG. 8A) andsensor efficiency (FIG. 9);

FIG. 24A shows the measured PHD (64-channels) obtained from a turbidsample containing fat emulsion (0.5% by volume) plus “spikes” of latexparticles (2.013- and 10.15-μm), without correcting for the effects ofsample turbidity on the signal voltage;

FIG. 24B shows the computed dPHD (successive subtraction) obtained fromthe PHD of FIG. 24A;

FIG. 24C shows the “raw” PSD (without correction for sensor efficiency)obtained from the computed dPHD of FIG. 24B, using the calibration curve(FIG. 8A);

FIG. 25A shows the measured PHD (64-channels) obtained from the samesample used in FIG. 24A, but with the baseline signal level raised toits normal level in the absence of turbidity;

FIG. 25B shows the computed dPHD (successive subtraction) obtained fromthe PHD of FIG. 25A;

FIG. 25C shows the “raw” PSD (without correction for sensor efficiency)obtained from the computed dPHD of FIG. 25B, using the calibration curve(FIG. 8A);

FIG. 26A, FIG. 26B, and FIG. 26C are block diagrams disclosing threetechniques that can be used to compensate for the effects of sampleturbidity on the signal generated by the new LE-type sensor;

FIG. 27A shows the measured PHD (32-channels) obtained for an aqueousslurry of silica (fully concentrated) used for CMP processing;

FIG. 27B shows the computed dPHD (successive subtraction, validpulse-ht. region, expanded scale) obtained from the PHD in FIG. 27A;

FIG. 27C shows the PSD (concentration, expanded scale) obtained from thecomputed dPHD in FIG. 27B, using the calibration curve (FIG. 8A) andsensor efficiency (FIG. 9);

FIG. 28A shows the measured PHD (32-channels) obtained for the samesilica slurry sample used in FIG. 27A, but with an added,low-concentration “spike” of 0.993-μm latex particles (1.30×10⁵/ml);

FIG. 28B shows the computed dPHD (successive subtraction, expandedscale) obtained from the PHD in FIG. 28A;

FIG. 28C shows the PSD (concentration, expanded scale) obtained from thecomputed dPHD in FIG. 28B, using the calibration curve (FIG. 8A) andsensor efficiency FIG. 9);

FIG. 29 is a block diagram showing the first, preferred embodiment ofthe invention;

FIG. 30 is a block diagram showing the second embodiment of theinvention;

FIG. 31 is a block diagram showing the third embodiment of theinvention;

FIG. 32 is a block diagram showing the fourth embodiment of theinvention.

FIG. 33 is a block diagram showing the fifth embodiment of theinvention; and

FIG. 34 is a block diagram showing the sixth embodiment of theinvention.

DETAILED DESCRIPTION OF THE INVENTION

The apparatus and method of the present invention is implemented by asensor, based on either light extinction or scattering, for counting andsizing particles in a fluid suspension. A quantity of the suspension iscaused to flow through the new sensor at a controlled flow rate within aconfined, well-defined measurement flow channel. Like its conventionalprior art counterpart, the new sensor responds to the passage ofindividual particles through an “optical sensing zone,” or OSZ.Therefore, like its predecessor, it is also classified as asingle-particle optical sensing (SPOS) device. However, as will beevident from the description to follow, the characteristics of this newsensor differ markedly from those obtained using the conventional SPOSapproach. For simplicity, most of the description to follow will berelated to a new light-extinction, or LE-type, sensor. However, withsimple modification the new apparatus and method can be used equallyeffectively to implement a light-scattering, or LS-type, SPOS device, aswill be discussed. Each of the new sensors, whether LE- or LS-type, isdesigned to function effectively at significantly higher concentrationsthan its conventional SPOS counterpart, and also to providesignificantly higher sensitivity.

Achieving a significant increase in the coincidence concentration of anSPOS sensor requires making a similarly significant reduction in thevolume, V_(OSZ), of the OSZ. There is a practical limit on the extent towhich the depth, b, of the flow channel 10 can be decreased as a meansof reducing V_(OSZ), in order to avoid frequent clogging of flow channel10 by over-size particles. Therefore, a substantial reduction in thecross-sectional area, A₀, of the incident light beam that illuminatesthe fluid-particle mixture in the flow cell and impinges on detectorD_(LE) is required. Of course, there is an important additionaladvantage that results from reducing the illuminated area, A₀—asubstantial reduction in the minimum detectable particle diameter. Aparticle of given size that passes through the center of the OSZ willmomentarily “block” (i.e., refract, reflect, scatter and absorb) alarger fraction of the total light incident on the flow cell anddetector, the smaller the parameter A₀.

The principal defining characteristic of the new SPOS method is notsimply a significant reduction in the size of the illuminated area, A₀,resulting in a significant reduction in Vosz and improvement insensitivity. Rather, it concerns the nature of the illuminating beam andthe resulting OSZ thereby defined. As is shown in FIG. 3, there are twoimportant and novel features inherent in the optical design. First, theincident beam alone (in conjunction with the front and back windows 36and 37 of the measurement flow channel 35) defines the OSZ. The sidewalls 38 and 39 that confine the fluid-particle suspension along thex-axis (FIG. 3) are no longer of any consequence with respect todefinition of the OSZ. Second, the physical volume associated with theOSZ can no longer be described by a single value; rather, it now dependson the size of the particles being measured.

The new approach, which is shown schematically in FIG. 3, is toilluminate measurement flow channel 35 with a light beam 41 from a laserlight source 40 which is focused by a lens 42 to form a beam 44 ofrelatively narrow cross section—i.e., smaller than the typicalilluminated width, a, of the flow cell in a conventional LE-type sensor(FIG. 1). The resulting OSZ is therefore defined approximately by a“pencil” beam of light 46, together with the front and back windows ofthe flow cell, separated by dimension “b.” The schematic diagram in FIG.3 provides a simplified picture of the OSZ defined by focused light beam46. First, the region of illumination that comprises the OSZ is notsharply defined, as implied by the approximately cylindrical zoneindicated in FIG. 3. Rather, the outer boundary of the OSZ is “fuzzy,”extending well beyond the zone indicated, as discussed below. Second,the beam passing through the flow channel 10, assuming that it has beenfocused, is typically is not uniform in width. Rather, in the case of afocused beam, its width varies over the depth of the measurement flowcell 35. The extent to which the beam waist varies over the depth of thechannel depends on the depth of field of the focused beam, defined asthe distance (y-axis) between the points at which the beam waist growsto {square root}2 times its minimum value. Ideally, the depth of fieldis significantly greater than the channel thickness, b, resulting in arelatively uniform beam width throughout the flow channel.

Consequently, there is a fundamental change in the physical design ofthe new sensor, quite apart from the radically different intensityprofile of the illuminating light. In the conventional design, thephysical width of the flow channel 10 and the effective width (x-axis)of the OSZ are one and the same, equal to dimension “a.” By contrast,the physical width of the flow channel in the new sensor (also definedas “a”) is typically much larger than the nominal width, 2w, of theincident light beam and therefore has no significant influence on theOSZ. Hence, the spacers (or shims) 38 and 39 that separate the front andback windows 36 and 37, determining the depth, b, of the flow cell (andOSZ), no longer need to be opaque or smooth on an optical scale to avoidscattering by the edges. This is a significant advantage, makingfabrication of the flow cell easier and less expensive.

It is usually convenient and effective to employ a “circularized” lightbeam, in which the incident intensity ideally depends only on the radialdistance, r, from the beam axis (coincident with the y-axis, with x=z=0,as seen in FIG. 3). Typically, one employs a “gaussian” light beam—i.e.one having a gaussian intensity profile, described in the focal plane(minimum beam waist), at y=b/2, byI(r)=I ₀ exp(−2r ² /w ²)  (7)where r²=x²+z² for the assumed circular beam.

Quantity 2w is the diameter of an imaginary cylinder containing most ofthe incident light flux. The intensity on its surface equals 1/e², wheree is the base for natural logarithms, or 0.135 times its value, I₀, atthe center of the beam (r=0). Essentially 100% (apart from losses due toreflections at optical interfaces and extinction by particles in thebeam) of the light flux contained in the incident beam traverses thefluid-particle mixture in the flow channel and impinges on the distantdetector D_(LE). This causes detector D_(LE) to provide a lightextinction signal V_(LE) in the form of a downwardly extending pulse,resembling pulse 30 in FIG. 2 at the output of I/V converter amplifier34.

This behavior is in sharp contrast to the illumination scheme employedin a conventional LE-type sensor. There, the starting light beam isexpanded greatly along the lateral (x) axis of the flow cell, so thatits width (1/e² intensity) is much larger than the width, a, of thefront window (and OSZ). As a result, there is relatively littlevariation in the incident intensity along the x-axis (i.e. for y=z=0)where the beam enters the flow cell, because the light is captured atthe top of the x-expanded gaussian beam. Therefore, a particle passingthrough the OSZ will experience substantially the same maximum beamintensity (i.e. at z=0), regardless of its trajectory. The specificvalues of x and y defining the trajectory ideally have no influence onthe resulting sensor response, i.e. the pulse height.

The contrast between the conventional optical design and the schemeemployed in the new sensor could hardly be greater. In the new sensor,by deliberate design, there is a large variation in the incidentintensity as a function of position (x-axis) across the width of theflow channel. In the case in which the incident light beam has asymmetric (circular) gaussian profile, the intensity variation is givenby Equation 7, with r=x. The maximum intensity, I₀, is achieved at thecenter of the beam (x=z=0), where for simplicity x=0 represents themidpoint of the channel (with the side walls at x=±a/2). As noted, theintensity occurring at x=±w, z=0 is reduced substantially, to 0.135 I₀.The intensity drops steeply with increasing distance from the beam,falling, for example, to 0.018 I₀ at x=±2w, z=0 and 0.00033 I₀ at x=+4w,z=0.

The consequences for the light-extinction signal thus generated by thepassage of particles through the new OSZ are far-reaching. First, as fora conventional LE-type sensor, the pulse height, ΔV_(LE), generated bypassage of a particle through the OSZ in general increases withincreasing particle size, all other factors being equal. In general, thelarger the particle, the larger the fraction of light “removed” from theincident beam, thus unable to reach the detector D_(LE). However, withthe new sensor the fraction of light removed from the beam now dependson the precise trajectory of the particle—specifically, the minimumdistance, |x|, of the particle to the center of the beam, x=0. (To firstapproximation, the response of the sensor will not vary significantlywith changes in the y-axis value of the trajectory, assuming that thebeam width is approximately constant over the depth of the flow channel,given an appropriately large depth of field, as discussed above.)

For a particle of given size and composition (hereinafter assumed to bespherical and homogeneous, for simplicity), the maximum “signal,” orpulse height, is achieved when the particle passes through the center ofthe beam, x=0. A particle of given effective cross-sectional area, ΔA,blocks the largest amount of incident light at the center of the beam,where the intensity is greatest. Particles of identical size that passthrough the flow channel along different trajectories, with differentminimum distances, |x|, from the beam axis, are exposed to varying, butsmaller, maximum levels of illumination. The greater the distance fromthe beam axis, the lower the integrated intensity incident on a particleand, hence, the less light flux removed from the beam, and the smallerthe resulting pulse height. The response therefore consists of acontinuous “spectrum” of pulse heights, ranging from a maximum value,for trajectories that pass through the center of the beam, toessentially zero (i.e. indistinguishable from noise fluctuations), fortrajectories located very far from the incident beam (|x|>>w). Themaximum pulse height depends on the beam waist, 2w, and the size of theparticles, as well as in some cases the refractive indices of theparticles and surrounding fluid. (This depends on the extent to whichlight scattering is significant relative to refraction and reflection incontributing to the overall light extinction signal.) A crucialassumption is that the particle trajectories are distributed randomly(i.e. occur with equal frequency) within the flow channel. Thisassumption is usually valid, given the typical dimensions of the flowchannel and the relatively low flow rates utilized. It is also assumedthat the number of particles passing through the sensor is sufficientlylarge that the statistical fluctuations in the number of particleshaving trajectories with any given x-axis value (i.e. over any (narrow)range of x values) can be ignored.

The relationship between particle size and pulse height for the newsensor is therefore radically different from that obtained for a sensorof conventional design. In the latter case, particles of a given size(and composition) give rise to pulses of nearly uniform height,irrespective of their trajectories. This behavior is the most importantgoal of sensor design for the conventional SPOS method. The typicallysmall variations in pulse height that occur, for example, when measuringpolystyrene latex “standard” particles of essentially uniform size arecaused by variations in the incident beam intensity within the OSZ alongthe x- and y-axes, for a given z-axis value. These variations ultimatelydetermine the resolution of the sensor. The resulting width of the PSDis therefore mostly a consequence of residual non-uniformity ofillumination across the OSZ, rather than an actual range of particlediameters.

By contrast, there is an obvious deterioration in the particle sizeresolution for the new sensor design. When a single particle passesthrough the sensor, it gives rise to a light-extinction pulse with aheight, ΔV_(LE) that can vary between a given maximum value andessentially zero. Conversely, given a single detected pulse, it isimpossible to determine the size of the particle that has produced it,solely from knowledge of the pulse height. For example, a particle thatis relatively small, but which passes directly through the beam axis,yields the maximum pulse height possible for a particle of that size(and composition). Alternatively, a particle that is much larger butwhich passes relatively far from the beam axis yields a pulse heightthat could actually be the same, depending on its size and trajectory.Even though the large particle is able to intercept a much larger areaof incident illumination than the small one, the average intensityincident on it is smaller than the intensity incident on the smallparticle. Hence, the resulting pulse height could turn out to be thesame as that produced by the small particle. Obviously, there are aninfinite number of pairs, {d, |x|}, of particle diameters and minimumbeam-trajectory distances that can give rise to the same pulse height.The particle diameter, d, and the resulting pulse height, ΔV_(LE), areeffectively “decoupled” from each other. This is the problem of“trajectory ambiguity” alluded to above in the Description of RelatedArt, which for more than twenty years has motivated the search for newlight-scattering based schemes for particle size determination usinggaussian beams.

The effects of trajectory ambiguity described above would appear torender the new narrow-beam sensor relatively useless for demandingparticle-sizing applications. Happily, such a pessimistic assessment isnot justified. The resolution of the new LE-type sensor is poor only ifone insists on using the new method to obtain the size of a singleparticle, or a relatively small number of particles. As will bedemonstrated, the apparently poor size resolution associated with thenew sensor can be restored to a very acceptable level by means ofappropriate mathematical deconvolution of the pulse-height data. Theresulting dramatic improvement in the effective sensor resolution ispossible by virtue of the fact that the new sensor is intended to beexposed to a large, statistically significant number of particles ofevery relevant diameter, or range of diameters, contained in the sampleof interest. This is the circumstance that renders the new sensingmethod very useful for particle size analysis, in sharp contrast to thesituation that holds for “contamination” applications. There, the sensoris exposed to relatively small numbers of particles of any given size,for which statistical significance is often not achieved.

The “raw” response of the new focused-beam sensor, like its conventionalSPOS predecessor, consists of the pulse height distribution (PHD)—ahistogram of particle “counts” vs pulse height, ΔV_(LE) . Thepulse-height scale is typically divided into a relatively large number(e.g. 32, 64 or 128) of “channels,” or “bins,” each of which encompassesan appropriately narrow range of pulse height voltages, thus definingthe voltage resolution of the PHD. It is usually convenient to establishchannels that are evenly spaced on a logarithmic voltage scale.Measurement of a new pulse causes the number of particle counts storedin the appropriate pulse height channel in the histogram to beincremented by one. Data are ideally collected from the particlesuspension of interest for a sufficiently long time that the resultingPHD becomes statistically reliable, and thus smooth and reproducible.This means that the number, N_(I), of particle counts collected in theI-th pulse-height channel is statistically significant, dominating thefluctuations due to statistical “noise,” for all I, e.g. for 1≦I≦128, inthe case of 128 channels. Assuming Poisson statistics, this means thatN_(I)>>{square root}N_(I) for all I.

A representative example of a PHD produced by the new LE-type sensor isshown in FIG. 4. The sample consisted of a 10,000:1 (by volume) aqueousdilution of a stock suspension of uniform polystyrene latex particles(Duke Scientific, Palo Alto, Calif.) of diameter=1.588 micrometers (em).The PHD was generated by a total of 83,702 particles during a datacollection time of 48 seconds. The flow rate utilized was 20 ml/min,resulting in a total analyzed sample volume of 16 ml and an averagepulse rate of 1,744/sec. The concentration of the stock suspension was1% by weight. Given a particle volume, V_(P), equal to 2.10×10⁻¹² cm³,and a density, p, of 1.05, this is equivalent to a number concentrationof 4.54×10⁹ per ml. After dilution, the particle concentration flowingthrough the sensor was 4.54×10⁵/ml. This value is much higher—indeed,more than 50 times higher—than the concentration levels that aretypically recommended for conventional LE-type sensors (i.e. to avoidsignificant coincidence effects). In fact, this concentration could havebeen increased substantially (at least 2-fold) without introducingsignificant distortion in the shape of the PHD due to coincidenceeffects.

Such high levels of particle concentration are possible only because thenew sensor responds to only a smallfraction of the total number ofparticles passing through it. Using the example of FIG. 4, the totalnumber, N_(T), of particles that passed through the sensor wasN_(T)≈4.54×10⁵/ml×16 ml, or 7.26×10⁶. The number, N_(P), of particles towhich the sensor actually responded, thus yielding the PHD of FIG. 4,was 83,702. Hence, the fraction, φ_(d), of particles of diameter d=1.588μm that actually contributed to the measured PHD, defined byφ_(d)=N_(P)/N_(T), was 1.15×10⁻², or 0.0115. Fraction φ_(d) is referredto as the “sensor efficiency.”

The fact that the sensor efficiency is so relatively small is notsurprising. In the case of a tightly focused beam, the width, a, of theflow channel is invariably much larger than the nominal width, 2w, ofthe focused beam. Therefore, most of the particles passing through thesensor are exposed to negligible levels of light intensity, becausetheir trajectories are located so relatively far from the beam axis—i.e.|x|>>w. Consequently, only a small fraction of the total number ofparticles are able to “block” enough light to give rise to detectablepulses, relative to the prevailing noise level. The great majority ofparticles pass undetected through the sensor.

While this limitation may appear to be serious, in practice it is oflittle concern, for two reasons. First, the fraction, φ_(d), ofparticles that produce detectable, measurable pulses will be fixed for agiven sensor width, a, even though the value changes with particlediameter, d. Second, the new sensing method is intended for use indetermining the particle size distribution (PSD) for samples that, bydefinition, are highly concentrated to begin with. Even followingdilution, if required, the concentration of particles of any given size(i.e. within any (narrow) size range) is, by definition, relativelyhigh. Assuming a suitable flow rate and data collection time, theresulting PHD will possess an acceptable signal/noise ratio, with a lowlevel of statistical fluctuations. Hence, even though only a smallfraction of the available particles will contribute to the raw data, theresulting PHD will be representative of the much larger number ofparticles in the sample that are ignored. Therefore, a reliable andaccurate PSD, representative of the entire sample, will be obtained fromthe “inefficient” new sensor.

It is useful to estimate the width, 2w_(d), of the imaginary,approximately cylindrical volume surrounding the beam axis thatrepresents the effective OSZ for particles of diameter d. By definition,any particle that passes through this imaginary region will give rise toa pulse that can be detected and quantified (i.e. by its pulse height).This width, 2w_(d), is directly related to the sensor efficiency, φ_(d),and is defined by2W _(d)=φ_(d) ×a  (8)

The PHD shown in FIG. 4 was obtained from a sensor having a flow channelwidth of 2 mm, or 2000 μm. From Equation 8, one therefore obtains2w_(d)=23 μm for the case of 1.588-μm particles. The estimated beamwidth, 2w, for this same sensor was between 10 and 11 μm (discussedbelow). Hence, the effective width of the cylindrical-shaped OSZ, in thecase of 1.588-μm particles, is slightly larger than twice the nominalwidth of the gaussian beam.

Several additional features of the PHD shown in FIG. 4 are noteworthy.First, as a consequence of the fact that the particle trajectories spana large range of |x| values, passage of uniform particles through thesensor indeed results in a PHD containing a wide range of pulse heights.In this case, these range from the threshold of individual pulsedetection (dictated by the prevailing r.m.s. noise level), roughly 5millivolts (mV), to a maximum of approximately 326 mV for the nominal“end” of the distribution. (This excludes a small number of “outlier”pulses, due to agglomerates and over-size primaries that extend to 500mV). Given the uniformity of the particles, this 65-fold range of pulseheights can only be ascribed to differences in particle trajectory. (Toa first approximation, one can neglect variations in the beam width overthe depth of the flow channel, as discussed earlier.)

Second, as expected, the PHD is highly asymmetric, skewed greatly in thedirection of smaller pulse heights. Clearly, there are many particletrajectories that sample a large range of |x| values (and, hence, beamintensities), but only relatively few that probe the central portion ofthe gaussian profile, where the intensity is substantially uniform. ThePHD exhibits a broad, smooth upswing in the number of particles withincreasing pulse height, accelerating to a relatively sharp peak,followed by a dramatic decline to the baseline, representing zero pulseevents. This sharp “cut-off” at the upper end of the distributiondefines the maximum pulse height, referred to hereafter as ^(M)ΔV_(LE).In the case of the PHD shown in FIG. 4, this value is approximately 326mV. The counts collected at this maximum value represent particles thatpassed through, or very close to, the center of the beam—i.e.trajectories with x≈0—where the fraction of total incident light flux“blocked” by the particles is the largest value possible. The countscollected in smaller pulse height channels represent particles thatpassed further from the beam axis; the greater parameter |x|, thesmaller the resulting pulse heights.

The relationship between the particle trajectory and the resulting pulseheight is shown schematically in FIG. 5. Trajectory “A” gives rise toextinction pulses having the maximum pulse height, ^(M)ΔV_(LE),immediately preceding the upper cut-off of the PHD. Trajectories “B,”“C,” “D” and “E” located progressively further from the beam axis, giverise to pulses with correspondingly lower pulse heights andprogressively lower numbers of particle counts. Eventually, the numberof particle counts per channel approaches zero, as the pulse heightreaches the detection limit (≈5 mV), at the lower left-hand corner ofthe PHD plot shown schematically in FIG. 5.

As discussed earlier, the reproducibility of the PHD should depend onlyon the degree to which the number of counts contained in the variouschannels are large compared to statistical fluctuations. Therefore, the“reliability” (i.e. the smoothness and reproducibility) of the PHDshould depend on the total number of particles counted during ameasurement. For a given particle size there will obviously exist aminimum number of pulses that should be counted and analyzed, belowwhich the PHD should be expected to exhibit significant, irreproducible“structure” from one measurement to the next, due to statistical noise.Again, the PHDs produced by the new sensor have meaning only to theextent that relatively large, statistically meaningful numbers ofparticles of the same size are detected during the data collectionperiod. Only if this is true can one expect to obtain optimal,reproducible PHD results, and correspondingly accurate, representativeparticle size distribution (PSD) results derived from the latter usingthe methods discussed below.

In the case of the 1.588-μm latex standard particles used to generatethe PHD shown in FIG. 4, a second measurement of a fresh 16-ml volume ofthe same stock suspension yielded a very similar PHD result, with 83,327particles detected. The difference in the total number counted lies wellwithin the square root of the average value (289). One can tentativelyconclude that the number of particles sampled by the sensor for eachmeasurement was sufficiently large to yield PHDs of acceptablereproducibility (confirmed by overlaying two or more PHDs).

From the preceding discussion it is clear that exposing the new sensorto larger particles should yield a PHD that is shifted to larger pulseheights. Specifically, the maximum pulse height, ^(M)ΔV_(LE),corresponding to particle trajectories passing through, or very closeto, the beam axis, must increase. This is indeed the case, as shown inFIG. 6, comparing PHD “A,” obtained for d=1.588 μm, with PHD “B,”obtained for d=2.013 μm. The latter consisted of a 2000:1 dilution (vol)of a stock suspension of polystyrene latex spheres (Duke Scientific) ofconcentration 0.45% (wt), equivalent to 1.0×10⁹ particles/ml. PHD “B”was generated by a total of 83,481 particles, using the same datacollection time and flow rate utilized in FIG. 4 and thus resulted in anaverage count rate of 1,739/sec.

The shape of PHD “B” (2.013-μm) is clearly very similar to that of PHD“A” (1.588 μm). The only significant difference is the value of themaximum pulse height, ^(M)ΔV_(LE), which now occurs at 482 mV. The peakof PHD “B” appears to be somewhat sharper (i.e. narrower) than thatobserved for the smaller particles. However, this assessment is largelya matter of perception, given the fact that the pulse height channelshave equal width on a logarithmic voltage scale. Hence, a channellocated at a higher pulse height value (e.g. 482 mV) will contain awider voltage range than a channel located lower on the scale (e.g. 326mV).

To a first approximation, the PHD for d=2.013 μm can be derived from thePHD for d=1.588 μm simply by “stretching” the latter in linear fashionalong the x-axis to higher pulse-height values, so that the maximumcut-off “edges” of the two PHD curves coincide. This action isaccomplished by applying a multiplicative factor to the pulse heightvalues associated with each channel of PHD “A.” This factor is equal tothe maximum pulse height, ^(M)ΔV_(LE), for PHD “B” divided by thecorresponding value for PHD “A”—i.e. 482/326=1.48.

It is instructive to compare the PHDs obtained for a series of uniformparticle size populations, encompassing a wide range of particlediameters. Representative results for the individual PHDs obtained forstatistically significant numbers of polystyrene latex standardparticles ranging in diameter from 0.806 to 20.00 μm are shown in FIG. 7and summarized in Table I. (Note: PHDs of reduced, but acceptable,signal/noise ratio can be obtained for particles as small asapproximately 0.6 μm using the same sensor and optical parameters.) Eachof the PHDs shown in FIG. 7 was obtained by measuring 16-ml ofappropriately diluted stock suspension, using a flow rate of 20 ml/min,as before. The maximum pulse heights, ^(M)ΔV_(LE), are expressed asabsolute (mV) values and also as percentages of 5 volts, or 5000 mV (the“baseline” voltage, V₀). This is the maximum possible pulse height,representing 100% extinction of the incident light flux. Each PHD inFIG. 7 is plotted as a relative-number distribution—i.e. the number ofcounts in each channel divided by the total number of counts collectedfor the sample in question.

As discussed above, any given PHD (e.g. “C”) in FIG. 7 can beapproximated by taking the PHD for the nearest smaller size (i.e. “B”)and shifting it to larger pulse-height values using an appropriatemultiplicative factor, ^(M)ΔV_(LE)(“C”)/^(M)ΔV_(LE)(“B”). This ispossible because of the self-similarity of the PHDs. This procedure isvery useful, as it can be used to compute, rather than measure, areasonably accurate PHD for any arbitrary particle size lying betweensizes for which PHDs have already been measured. This operation is animportant ingredient in the mathematical procedure used to “deconvolute”measured PHDs, as will be discussed below.

It is clear from FIG. 7 (and Table I) that the PHD produced by the newsensing method for uniform-size particles is able to detect relativelysmall changes in particle diameter. The maximum pulse height,^(M)ΔV_(LE), increases significantly with increasing particle size overa relatively wide (i.e. >25-fold) size range, as shown in FIG. 8A.Indeed, one can make the seemingly contradictory argument that the size“resolution” of the new sensing method is, in fact, relatively high,notwithstanding the fact that the PHD produced by particles of a givensize is broad and, by definition, lacking in resolution. This point ofview will become evident below in connection with the procedures used to“invert,” or deconvolute, the PHD data obtained from a mixture ofparticles of different sizes, in order to obtain the final object ofinterest, the PSD. For the time being, it is sufficient to point outthat the results of FIG. 7 demonstrate that a relatively small change inthe particle size yields a significant, measurable difference in thevoltage associated with ^(M)ΔV_(LE). As will be seen below, thischaracteristic of the signal response is a necessary (although notsufficient) condition, permitting the deconvolution procedure to beeffective in extracting a PSD of relatively high resolution from themeasured PHD.

It is instructive to compare the measured light-blocking ratios—i.e.^(M)ΔV_(LE) expressed as a percentage of the maximum saturation value,V₀, of 5 Volts—with the values predicted by a naïve light-blockagemodel. This assumes that a particle effectively removes 100% of thelight incident on it, over a circular disk of area πd²/4, regardless ofits size, ignoring the contribution to the LE signal made by lightscattering, which dominates at sufficiently small sizes. This comparisonis shown in FIG. 8B, with three sets of model calculations, assuminggaussian beam widths of 10-μm (open squares), 11-μm (open circles) and12-μm (open triangles). (These values are consistent with an independentmeasurement of the beam waist using a moving-slit beam profiler: 12±2μm.)

As can be seen in FIG. 8B, the measured values of ^(M)ΔV_(LE) (solidcircles), expressed as percentages of the maximum value possible (5Volts), for d=5.03- and 10.15-μm are in closest agreement with assumedbeam widths of 10-μm (open squares) and 11-μm (open circles). An averagevalue of 10.5-μm therefore represents the best estimate. At the upperend of this 5-10 μm size range, simple light refraction should dominatethe light extinction phenomenon. Below 5-μm, the agreement is not asgood, deteriorating progressively as the particle size decreases. Thetheoretical values in this region should indeed be lower than themeasured ones, because the naïve model employed ignores the effects oflight scattering. The smaller the particle, the greater the relativecontribution of scattering to the overall LE signal and hence thegreater the extent of the discrepancy between theory and measurement, asobserved.

Given an effective beam width of approximately 10.5-μm, the value foundfor ^(M)ΔVLE should approach “saturation” for particles significantlylarger than this size. Specifically, there is a diminishing fraction oftotal light flux in the beam remaining to be blocked by a 20-μm particlethat has not already been extinguished by a 10-μm particle passingthrough the center of the beam. Hence, the slope of ^(M)ΔV_(LE) vs d,whether measured or calculated, “rolls over” with increasing d,asymptotically approaching 100% for d values larger than about 10-μm. Atthe small-diameter end of the scale, the slope of ^(M)ΔV_(LE) vs ddecreases with decreasing d, owing to the diminishing contribution ofscattering to the LE signal. Therefore, the shape of the curve of thelight-blocking ratio over the entire size scale resembles a sigmoid.Unfortunately, the agreement between the measured and calculatedlight-blocking ratios at d=20 μm is not nearly as good as that obtainedfor 5.03 and 10.15-μm. The calculated ratios for beam widths of 10- and11-μm are 99 and 98%, respectively, while the measured ratio is “only”90%. The likely source of this discrepancy is an imperfect beamintensity profile, deviating significantly from the ideal gaussian shapeassumed by the model. The existence of imperfect optical elements,incomplete beam circularization and possible misalignment can result inan asymmetric pattern of lower intensity light regions surrounding thehigh intensity region of the beam. Light rays corresponding to thesenon-ideal regions can reach the detector even if most of the raysassociated with the main beam are effectively blocked by a largeparticle. Hence, passage of a 20-μm particle through the beam axisresults in extinction of less than 100% of the incident light.

It is important to appreciate the dependence of the sensor efficiency,φ_(d), on the particle diameter, d. The larger the particle, the largerthe fraction of incident light flux that it is able to intercept and“block.” Hence, a large particle can be detected further from the beamaxis than a smaller particle, which may vanish, even though it followsthe same trajectory as the larger particle, or even one closer to thebeam axis. Therefore, it should be evident that the fraction ofparticles that are detected and contribute to the PHD, defined as φ_(d),increases with increasing particle size (excluding the effects ofnon-monotonic variations of the scattering intensity with particle size,described by Mie scattering theory).

FIG. 9 shows representative values of φ_(d) vs d obtained forpolystyrene latex particles in the size range of 0.806- to 20.0-μm,based on the results shown in FIG. 7 and Table I. In order to calculatethe various φ_(d) values, it was necessary to determine independentlythe total number of particles that passed through the sensor duringmeasurement of the respective PHDs. These values were determined bymeasuring a known volume of each suspension, diluted by a suitable (muchlarger) factor, using a conventional sensor (based on a combination ofLE and LS methods), having approximately 100% counting efficiency. Thevalue of φ_(d) for each diameter, d, was obtained by dividing the numberof particles counted during a PHD measurement by the total number ofparticles present in the volume of suspension that flowed through thesensor.

As shown in FIG. 9, the value of φ_(d) decreases monotonically withdecreasing particle diameter, from 0.030 for d=20.0-μm to 0.0053 ford=0.0806-μm, representing a nearly 6-fold decrease. The effective widthof the OSZ shrinks with decreasing particle diameter, as expected. Theefficiency of the new sensor “rolls over” and declines precipitouslytoward zero with increasing slope when the particle size falls belowabout 1.5-μm. This feature simply confirms the inability of the LEmethod, even with a beam width as small as 10-μm, to functioneffectively when the particle size is sufficiently small. This is thepoint at which it becomes useful to employ the LS method (discussedbelow). However, it is also clear from FIG. 7 that the PHD resultspossess good signal/noise ratios for particle diameters as small as0.8-μm (or smaller.

Because w_(d) is proportional to φ_(d), it is clear that the width ofthe effective OSZ increases with the particle diameter in the same waythat φ_(d) increases with d, as shown in FIG. 9. As discussed above, theinfluence of the light beam extends further across the flow cell alongthe x-axis the larger the particle in question. This can be consideredto be a “non-linear” response of the new sensor, in which its efficiencyin general increases with particle diameter. This behavior will be seento have important implications for the procedure of obtaining thedesired PSD by deconvolution of the PHD, especially for samplescontaining a broad range of particle sizes.

From Equation 8 it is clear that decreasing the width of the flowchannel can increase the sensor efficiency for all diameters. This wouldallow a larger (albeit still small) fraction of the particles to passthrough the region of influence of the light beam—i.e. the effectiveOSZ. Hence, in principle the sensor efficiency for particles of allsizes can be improved simply by decreasing dimension “a.” However, inpractice there are two reasons why it may not be useful or advisable tocarry out such an “improvement.”

First, a reduction in dimension “a” implies a corresponding reduction inthe cross-sectional area of the flow channel, A_(F)=a×b. However, thereis a practical limit on how small this area can be without presentingexcessive impedance to the flow of the sample suspension. Also,reduction in this dimension can give rise to errors in the measuredpulse heights, owing to the high resulting velocity of the particles.For a given flow rate, F, the velocity of the particles passing throughthe OSZ varies inversely with dimension “a” (Equation 4). If thevelocity is too high, the resulting signal pulses will becomecorrespondingly narrower in time, potentially leading to errors (i.e. areduction) in the measured pulse heights associated with the bandwidthof the amplifier means. One could avoid this problem by reducing theflow rate. However, this action would reduce the statistical accuracy ofthe resulting measured PHD—i.e. proportionately fewer particles of eachrelevant size would be detected during a given period of time.

Alternatively, one might consider increasing the depth, b, of the flowchannel as a means of compensating for a decrease in the width, a, inorder to keep quantity AF substantially constant and thereby restore theparticle velocity to an acceptable value. However, this action wouldproduce two negative consequences. First, the volume of the effectiveOSZ for each particle size would increase in proportion to the increasein “b” (assuming no change in the effective width of the OSZ). Thecoincidence concentration would decrease by the same factor as theincrease in “b,” thus negating the advantage of the new sensor in beingable to accommodate relatively concentrated suspensions. Second, asignificant increase in “b” would result in reduced resolution of thePHD and the resulting PSD, owing to greater variation in the width ofthe beam (assuming that it is focused) and effective OSZ over the depthof the flow channel. Broadening of the ideally sharp “cut-off” of thePHD at the maximum pulse height, ^(M)ΔV_(LE), would result in reducedresolution of the PSD obtained by deconvolution of the PHD.

Therefore, it is not realistic to increase greatly the sensor efficiencyby one or more of the means reviewed above. Fortunately, this“limitation” in performance is, in practice, not the shortcoming that itappears to be. In fact, in at least one important respect, it is avirtue. First, as discussed above, the new sensor is intended to beexposed to relatively concentrated samples. The small fraction (e.g.0.005 to 0.03, from FIG. 9) of particles detected still translates tolarge absolute numbers of particles of each size that contribute to thePHD. Second, and more important, the relatively low sensor efficiencyprovides a significant advantage for applications requiring predilutionof the starting sample suspension. The coincidence concentration valuesfor the new sensor are larger than the corresponding value achieved by aconventional LE-type sensor by roughly a factor of 1/φ_(d)—i.e.approximately 30 to 200 times greater, based on the values shown in FIG.9. (This comparison assumes that the beam width, 2w, and flow channeldimensions, a and b, are the same for the traditional LE-type sensor.)Therefore, a concentrated suspension needs to be diluted much less—i.e.a factor 1/φ_(d) less—than what is required by a conventional sensor.Consequently, the diluent fluid (e.g. water, organic solvent, etc.) canbe correspondingly “dirtier” (with respect to contaminant particles)than the diluent fluid normally used. In practice, this is an importantadvantage.

From the previous discussion and the results shown in FIGS. 8A and B, itis evident that the new sensor has diminishing resolution for particlediameters significantly larger than the width of the beam. Here, theterm “resolution” refers to the change in ^(M)ΔV_(LE) for a given (unit)change in particle diameter—i.e. the slope of ^(M)ΔV_(LE) vs d. At thesmall end of the size scale, this slope, and hence the resolution,decreases with decreasing d. The threshold for detection of the smallestparticles is determined by the smallest pulse height, ΔV_(LE) that canbe measured, given the prevailing noise fluctuations. It should beappreciated that the range of particle diameters over which the newsensing method yields results of acceptable resolution depends on thechoice of beam width, all other variables being equal. If the beam widthis increased significantly, the region of maximum slope of ^(M)ΔV_(LE)vs d—i.e. the point of inflection of the curve—will shift to largerparticle sizes; the larger the beam width, the larger the shift. Thesensor can then be effectively employed to obtain PSDs with acceptableresolution for larger particles. In summary, the PHD response obtainedusing the new sensing method can be “scaled” to larger particlediameters, based on the choice of beam width. The influence of the beamwidth on the calculated sigmoidal curves of ^(M)ΔV_(LE) vs d (assuming100% light extinction) is shown in FIG. 10. The beam widths utilizedinclude 6-μm (open circles), 9-μm (open squares), 12-μm (opentriangles), 15-μm (closed circles), 18-μm (closed squares) and 21-μm(closed triangles). The range of acceptable resolution, corresponding tomaximum pulse heights in the range of 10 to 90% of saturation, in thelast case has shifted to 5-30 μm.

Conversely, if the beam size is reduced significantly, the point ofmaximum slope of ^(M)ΔV_(LE) vs d will shift to lower diameters.However, it should be appreciated that there is not a correspondinglysignificant reduction in the minimum size of particles that can bedetected. In theory, the value of ^(M)ΔV_(LE) for a given (small)particle diameter will increase with decreasing beam width. In practice,however, there are limitations on the improvement in performance thatcan be achieved by a new LE-type sensor at the low end of the particlesize scale. First, there is a limit, imposed by diffraction theory, onhow small a beam can be achieved. At this size—in practice, 3-5 μm—thedepth of field of a focused beam will be very narrow, requiring the useof a prohibitively thin flow channel in order to obtain the minimalacceptable variation in beam width (and thus OSZ width) over the depthof the channel. Given realistic values for the channel depth (i.e. b>100μm), to avoid frequent clogging, a significant variation in the beamwidth over the depth of the channel is unavoidable. This will negativelyimpact the sharpness of the maximum pulse height cut-off and theresolution of the resulting PSD.

Second, at the small end of the particle size scale the light scatteringmechanism will dominate the LE signal. Despite the diminished width ofthe focused beam, the absolute fraction of the incident light fluxeffectively removed from the beam will be very small and will decreasewith the particle diameter. In theory, the presence of an arbitrarilyhigh background signal level, V₀, should not affect the ability of thedetector and associated electronic system to detect a pulse of verysmall height, superimposed on V₀. In practice, however, there is a lowerlimit on the value of ΔV_(LE) that can be measured, because offluctuations in V_(LE), due to a variety of “noise” sources associatedwith the light source, detector, signal-conditioning means and powersupply. Contaminant particles in the sample suspension also contributeto fluctuations in the measured signal. When the pulse height fallsbelow a certain value, the pulse effectively disappears—i.e. it isindistinguishable from the fluctuations in V_(LE) caused by these noisesources.

Consequently, increasing the sensitivity, using the new method ofilluminating particles in a confined space with a narrow focused lightbeam, requires changing the mode of detection from light extinction tolight scattering (LS). The signal that results when a particle passesthrough the OSZ will then depend on the magnitude and angulardistribution of the scattered light intensity produced by the particleover a selected range of scattering angles. The useful signal pulse willno longer be burdened by a high background light level associated withthe incident light beam, as is the case for the LE method. The opticalscheme that is typically used to implement the new LS measurement issimple, shown schematically in FIG. 11. In many essential respects—i.e.,including the light source 40, focusing optics 42 and thin measurementflow channel 35—the apparatus is the same as that used for the newLE-type sensor (FIG. 3). In particular, one typically utilizes a narrowfocused light beam 46 with a gaussian intensity profile that passesthrough the thin dimension, b, of the flow channel—essentially the samescheme as that utilized for the new LE-type sensor. The only way inwhich it typically might differ is that the width of the beam, 2w, mightbe chosen to be smaller than that used for the new LE-type sensor, inorder to achieve a higher sensitivity.

The main design difference that distinguishes the new LS-type sensorfrom its LE counterpart is the addition of a light collectionmeans—typically one or more lenses—in order to gather scattered lightrays originating from individual particles passing through the OSZ,created by the incident light beam. The lens system is designed tocollect scattered light over a particular, optimal range of angles,typically encompassing relatively small angles of scattering. In thescheme shown in FIG. 11, a mask 50 has been placed in front of the firstcollection lens. Mask 50 comprises an outer opaque ring 52 and an inneropaque area 54, which form a transparent ring 56. Mask 50 allows onlylight rays with scattering angles, θ, located within an imaginaryannular cone defined by angles θ₁ and θ₂ (i.e. θ₁≦θ≦θ₂) to impinge onthe first collection lens 62. Typically, this lens is centered on theaxis of the incident beam, at an appropriate distance (i.e. its focallength) from the center of the flow channel, causing a portion of thediverging scattered light rays from the OSZ to be captured by the lensand become approximately collimated. A second lens 64 can then be usedto focus the resulting parallel scattered rays onto a suitable(small-area) detector D_(LS). The resulting signal is “conditioned” byone or more electronic circuits, typically including the functions ofcurrent-to-voltage conversion and amplification.

As alluded to above, there is a crucial difference between the signal,V_(LS), created by this optical scheme and the signal, V_(LE), shown inFIG. 2, produced by the LE-type sensor. Unlike the latter, the LS-typesensor, by design, prevents the incident light beam emerging from theback window of the flow cell from reaching the detector, D_(LS).Instead, the incident beam is either “trapped” by means of a suitablesmall opaque beam “stop” (e.g., the inner opaque area 54) or deflectedby a small mirror away from the lens that is used to collect thescattered light rays originating from the OSZ. Consequently, therelatively large “baseline” level, V₀, necessarily present in theoverall signal, V_(LE), produced by the LE-type sensor is now absentfrom the LS signal, V_(LS). Ideally, the new “baseline” signal level iszero—i.e. there should be no scattered light generated from sourceswithin the OSZ in the absence of a particle. In practice, of course,there will be some amount of background light caused by light scatteredfrom the surfaces of the front and/or back windows of the flow channel,due to imperfections on, or contaminants attached to, the lattersurfaces. In addition, there may be fluctuating background light due toscattering from small contaminant particles suspended in the diluentfluid. Also, for some samples there may be fluctuations in backgroundlight produced by a “sea” of ultra-fine particles which comprise a majorfraction of the overall particle population, but which are too small tobe detected individually.

When a particle of sufficient size passes through the OSZ, defined bythe incident gaussian light beam and front and back windows of flowchannel 35, a momentary pulse occurs in the output signal produced bythe detector, D_(LS), and associated signal-conditioning circuit. Ingeneral, one might naïvely expect that the larger the particle, thegreater the amount of light scattered by it, assuming the sametrajectory, and therefore the greater the height of the signal pulse. Ifthis is the case, the output signal, V_(LS), will resemble that shownschematically in FIG. 12 for particles of increasing diameter, d₁<d₂<d₃,having the same value of |x|. In practice, the actual pulse heightdepends not only on the size of the particle, but also itscomposition—specifically, its index of refraction (and that of thesurrounding fluid) and absorbance, if any, at the incident wavelength.The pulse height also depends on the wavelength of the beam and theorientation of the particle as it passes through the OSZ, if it is notspherical and homogeneous. Finally, for particles comparable in size to,or larger than, the wavelength, the scattering intensity variessignificantly with the scattering angle. Consequently, in this case thepulse height depends on the range of angles over which the scatteredlight is collected and measured.

The relationship between the scattered light “radiation pattern” (i.e.intensity vs angle) and all of these variables is described by classicalMie scattering theory, which takes into account the mutual interferenceof the scattered light waves within the particle. In general, the largerthe particle, the more complex (i.e. non-isotropic) the angulardependence of the scattered intensity resulting from intra-particleinterference. In order to optimize the response and performance of theLS-type sensor, one must confine the collection of scattered light to arange of angles, θ, for which the net integrated response, ΔV_(LE),increases monotonically with the diameter, d, of particles of a givencomposition (i.e. refractive index) over the largest possible, orexpected, size range. This requirement can usually be satisfied bychoosing a range of relatively small angles, θ₁<θ<θ₂, close to theforward direction. In this way, one avoids “reversals” in the integratedscattering intensity with increasing particle size due to variations ofthe intensity with changes in angle, especially significant at largerangles as a consequence of Mie intra-particle interference.

There are two properties of the signal, V_(Ls), produced by the newLS-type sensor that are qualitatively different from the properties ofthe signal, V_(LE), produced by the corresponding LE-type sensor. First,the signal pulse caused by passage of a particle through the OSZ and the“overall” signal, V_(LS), are essentially the same in the case of theLS-type sensor. The relatively high background signal level thataccompanies the pulse of interest in the LE-type sensor is absent. (Thesame situation clearly holds for a conventional LS-type sensor. Thisconsists of the scheme shown in FIG. 1 with a similar addition of one ormore lenses and a detector means for collecting and measuring thescattered light originating from the OSZ over a range of angles,excluding the incident light beam.) Therefore, in the case of relativelysmall particles that give rise to pulses of low magnitude, thesignal/noise ratio achieved in practice using the LS method should besignificantly better than that realized using the LE method. Thisadvantage becomes more important the smaller the particle and the weakerthe resulting pulse, as the latter approaches the prevailing noisefluctuations. Another way of appreciating the inherent advantage of theLS method over its LE counterpart is to realize that the former is basedon “detection at null.” That is, quantitative detection of a pulseideally is carried out in the presence of zero background signal. From asignal/noise perspective, this is in sharp contrast to the situationthat obtains for the LE method, which requires high “common-moderejection.” The “common-mode” signal, V₀, is always present in the rawsignal, V_(LE), and must be subtracted, or otherwise suppressed, inorder to extract the (often small) signal pulse of interest.

There is a second important and distinguishing property of the LSsignal, V_(LS). The signal/noise ratio associated with the measurementof ΔV_(LS) can in principle be improved by increasing the power of theincident light beam, so as to increase the light intensity incident on aparticle at all points within the OSZ. Therefore, in principle one canreduce the lower size detection limit for the new LS sensor byincreasing the power of the light source, as for a conventional LSsensor. Eventually, a lowest size limit will be reached, based on noisefluctuations associated with the suspending fluid and/or the lightsource and detection system. Of course, as discussed above, the lowerparticle size limit can also be improved for the new LS-type sensor byreducing the width, 2w, of the incident beam, assuming no change in thepower of the latter. This action will obviously increase the maximumintensity incident on the particles that pass through the beam axis(x=0), and therefore the height of the largest resulting pulse for aparticle of given size, as well. However, this method of improving thesensitivity eventually reaches a point of diminishing return, due tolimitations imposed by diffraction theory (establishing a minimum beamwidth) and excessive variation of the focused beam width over the depth,b, of the flow cell due to excessively-long depth of field.

By contrast, an increase in the power of the light source has relativelylittle effect on the lowest particle size that can be measured using theLE method. For example, a doubling of the power of the light source willresult in a doubling of the baseline signal level (FIG. 2), to 2V₀. Theheight of the pulse, ΔV_(LE), produced by a particle of the same sizeand trajectory will also be doubled, assuming no change in the beamwidth. However, the root-mean-square magnitude of the noise fluctuationsassociated with the relatively high baseline signal level will typicallyalso be approximately doubled, because these fluctuations are usuallyassociated with the light source and therefore scale with the outputpower. Hence, one expects little or no improvement in the signal/noiselevel for the LE-type sensor. Consequently, there should be little or noreduction in the lower size detection limit achievable by the LE methodas a consequence of increasing the power of the light source. Animprovement will be realized only if the signal/noise ratio associatedwith the light source improves with increased power.

When uniform size particles flow through the new LS-type sensor,depending on their trajectories they are individually exposed todifferent values of maximum incident intensity, given by Equation 7,with r=x, z=0. (For simplicity, it can be assumed that the particles aremuch smaller than the beam width, so that every point in a givenparticle is exposed to the same intensity at any given time.) Therefore,as with the new LE-type sensor, the height, Δ_(VL)S, of the resultingpulse generated by a particle of given size depends on the distance,|x|, of closest approach (z=0) to the axis of the incident beam. Thesmaller the distance |x|, the larger the value of Δ_(VL)S. Hence, likeits new LE counterpart, the new LS-type sensor generates a distributionof widely varying pulse heights, Δ_(VL)S, when a suspension of uniformparticles passes through it at an appropriate flow rate. The shape ofthe resulting PHD bears a strong qualitative resemblance to the highlyasymmetric shape of the PHDs obtained using the new LE method,exemplified in FIGS. 4, 6 and 7. That is, the number of pulse counts(y-axis) is relatively small at the smallest measurable pulse height(just above the noise fluctuations) and rises with increasing pulseheight, Δ_(VL)S. The pulse count value culminates in a peak value at amaximum pulse height, referred to as ^(M)ΔV_(LS), corresponding toparticle trajectories for which |x|≈0. Above ^(M)ΔV_(LS) the number ofpulse counts ideally falls to zero, assuming that the particleconcentration is below the coincidence concentration (discussed earlier)for particles of that size, so that at most one particle effectivelyoccupies the OSZ at any given time. Of course, a PHD obtained using thenew LS method usually pertains to particles that are smaller—oftensignificantly so—than those used to generate a typical PHD using the newLE method.

As noted above, the shape of the PHD—number of pulse counts vsΔV_(LS)—generated for uniform particles using the new LS method isqualitatively similar to the shape of the PHD obtained for uniform(typically larger) particles using the new LE method. Both kinds of PHDsshare the distinguishing characteristic of a sharp “cut-off” followingtheir respective peak number of pulse counts, coinciding with theirmaximum pulse height values, ^(M)ΔV_(LS) and ^(M)ΔV_(LE). However, itshould be appreciated that there are quantitative differences in theshapes of the two kinds of PHDs, notwithstanding their qualitativesimilarities, even for the same particle size—e.g. d=1 μm. The “frontend” design of the new LS-type sensor—i.e. the focused light beam andrelatively thin flow cell—is essentially the same as that utilized forthe new LE-type sensor. Therefore, what distinguishes one type of sensorfrom the other concerns the means and manner of light detection and thetype and magnitude of the response pulses generated by each method, evenin the case of particles of the same size. For the new LS method, theresponse is due only to light scattering, and its magnitude, ΔV_(LS), isproportional to the intensity of the light incident on the particle, allother relevant variables being the same.

By contrast, for the new LE method the magnitude of the response,ΔV_(LE), is a more complex function of the intensity incident on theparticle. First, the response is due to a combination of physicaleffects—refraction (and reflection) plus light scattering. However, thescattering phenomenon asserts itself in an “inverse” sense. That is, asmall fraction of the incident light flux is removed from the beambefore it reaches the detector. Second, over the typical size range forwhich the new LE method is applicable, there is a substantial variationin the incident intensity across the particle. Therefore, it should notbe surprising that the fractional change of pulse height due to a givenchange in |x|, dependent on both particle size and trajectory, isgenerally different for the two methods. Similarly, the fractionalchange in pulse height with particle diameter, dependent on bothparticle size and trajectory, is also generally different for the twomethods. Rigorous application of the physical principles (Mie theory)underlying refraction, reflection and scattering for particles ofvarious sizes, combined with gaussian beam optics, would be required inorder to obtain reliable theoretical estimates of the detailed shapes ofthe PHDs generated by the two methods.

From the discussion above, it should be evident that the behavior of thenew LS-type PHDs with respect to changing particle size approximatesthat obtained for the new LE-type PHDs, exemplified by FIG. 7.Notwithstanding the differences in the detailed shapes of the newLS-type PHDs—number of pulses vs ΔV_(LS)—compared to new LE-type PHDs,the two types of PHDs share a common characteristic. There is aprogressive shift to higher pulse-height values of one PHD to the next,corresponding to larger particle diameter. In particular, and mostimportantly, the maximum pulse-height values, ^(M)Δ_(VL)S, increaseprogressively with increasing particle size. Of course, this behaviorassumes that the new LS-type sensor has been properly designed, with anappropriate range of detected scattering angles, precisely in order toensure a monotonic response of ^(M)ΔV_(LS) with d. There are twocompeting effects. On the one hand, the larger the range of angles overwhich scattered light is collected, the larger the resulting pulseheight, Δ_(VL)S, and hence the greater the signal/noise ratio forparticles of a given size, resulting in higher sensitivity—i.e. a lowerparticle size detection limit. On the other hand, the smaller both therange of scattering angles collected and the actual angles themselves,the smaller (and more benign) the effects of intra-particle Mieinterference. Consequently, it is less likely that “reversals” willoccur in the detected scattering intensity—i.e. non-monotonic behaviorof ^(M)ΔV_(LS) vs d over the desired size range.

As previously discussed for new LE-type PHDs, a new LS-type PHD for agiven particle diameter, d=d₂, can be constructed with reasonableaccuracy from a PHD measured for a smaller size, d=d₁, by “stretching”the latter to higher values of Δ_(VL)S, using an appropriate scalefactor. (Usually it is desirable to use a logarithmic pulse-heightscale—number of pulses vs log Δ_(VL)S.) This scale factor is given bythe ratio of the final and initial maximum cut-off pulse height values,^(M)ΔV_(LD)(d₂)/^(M)ΔV_(LS)(d₁). In practice, as with the new LE method,one can measure a set of new LS-type PHDs using a set of suspensions ofuniform particles that encompass the desired size range with appropriatediameter spacing. The PHD corresponding to any size between two measuredsizes can then be calculated by interpolating between the two adjacentmeasured PHDs using this linear stretching operation with an appropriatescale factor.

Finally, in addition to the similarity/difference in the shapes of thePHDs generated by the two new methods, there is another property of theresponse of the new LS-type sensor that is qualitatively similar to, butquantitatively different from, the corresponding property of the newLE-type sensor. This is the width of the effective OSZ, 2w_(d), and thecorresponding sensor efficiency, φ_(d), related to 2w_(d) and the flowchannel width, a, by Equation 8. As for the new LE-type sensor,parameter φ_(d) accounts for the fact that only a small fraction of thetotal number of particles passing through the sensor during datacollection are detected and therefore contribute to the PHD. The sameconcept involving an imaginary, approximately cylindrical OSZ describedabove in connection with the new LE-type sensor is equally valid for thenew LS-type sensor. For particles of a given diameter, the integratedscattered light intensity collected over a fixed, selected range ofscattering angles decreases with decreasing light intensity incident onthe particle. Therefore, the larger the distance, |x|, of closestapproach (i.e. z=0) of the particle trajectory to the axis of theincident beam, the smaller the magnitude of the response, ΔV_(LS). Atsome largest value of |x|, the pulse height will fall sufficiently thatthe pulse will effectively be indistinguishable from the prevailingnoise fluctuations in the overall signal, V_(LS), thereby rendering theparticle undetectable. This value of |x| thus defines the radius, w_(d),of the effective (approximately cylindrical) OSZ for particles of thegiven dianeter, d. The sensor efficiency for this size is then easilydetermined using Equation 8.

It should therefore be evident that the larger the particle diameter, d,the greater the distance of closest approach, |x|, of the particle tothe incident beam axis while still permitting its detection.Consequently, the larger the particle, the larger the width, 2w_(d), ofthe effective OSZ and, hence, the greater the sensor efficiency, φ_(d),for particles of this larger size. This monotonic relationship betweenφ_(d) (or 2w_(d)) and d presumes correct design of the new LS-typesensor, such that ΔVLS increases monotonically with d for particles of agiven composition over the size range of interest. Therefore, φ_(d) forthe new LS-type sensor will increase with d, as is the case of the newLE-type sensor. However, one should not expect that the increase inφ_(d) with d will obey the same relationship that was found for the newLE method, summarized in FIG. 9. Qualitatively, one may expect that thebehavior of φ_(d) vs d will be similar for both the new LS and LEmethods. Quantitatively, however, the details of this behavior should beexpected to differ for the two methods, due to fundamental differencesbetween the physical properties underlying scattering andrefraction/reflection (minus a small scattering contribution).

There is an additional, important difference in the behavior of the newLS response compared to its new LE counterpart, with respect to sensorefficiency. As already discussed, the sensitivity of the new LS-typesensor can be improved—i.e. the lower particle size limit reduced—byincreasing the power of the incident light beam, assuming that all otherdesign parameters are unchanged. Related to this improvement is anenhancement in the sensor efficiency, φ_(d). This is evident, given thefact that the pulse height, Δ_(VL)S, obtained for a given particle sizeand trajectory distance, |x|, will increase in proportion to theincrease in the light intensity incident on the particle. Hence, thetrajectory can be further from the beam axis than it could otherwise bewhile still permitting detection of the particle. Therefore, the width,2w_(d), of the effective OSZ and the corresponding efficiency, φ_(d),for particles of the same diameter, d, will increase (in some nonlinearfunctional fashion) with increasing power of the incident beam. Theresulting curve describing φ_(d) vs d (the counterpart of the plotobtained for the new LE-type sensor, shown in FIG. 9) will shift in somefashion to a set of higher φ_(d) values for each value of d.

In summary, with respect to the power of the incident beam, the behaviorof the new LS-type sensor differs both qualitatively and quantitativelyfrom the behavior of the new LE-type sensor, in at least two importantrespects. First, the lower size detection threshold for the new LS-typesensor in general increases with increasing incident beam power. Thisbehavior typically does not hold for the new LE-type sensor, unless thesignal/noise ratio associated with the light source also increases withthe power of the beam (or, using a different, “quieter” light sourceand/or detector and associated signal-conditioning circuit). Second, thesensor efficiency, φ_(d), associated with the new LS-type sensor ingeneral also increases with increasing incident beam power. Thisbehavior typically is not obtained for the new LE-type sensor, unlessthere is an improvement in the signal/noise ratio associated with theincreased power of the light source.

Finally, the PHD generated by the new LS-type sensor for particles of agiven size and composition will shift proportionately to higherpulse-height values if the power of the incident beam is increased. Thisaspect of the response generated by the new LS-type sensor thereforeimplies that the set of PHDs generated by a set of samples containinguniform particles of different size has quantitative significance onlywith reference to a particular incident beam power. If the power isincreased, the PHDs will shift correspondingly to higher pulse-heightvalues. Interestingly, this behavior is similar to that expected andobserved for the new LE-type sensor, albeit for a different reason. Ifthe power of the incident beam is increased by a given percentage, boththe “baseline” voltage, V₀, and the pulse height, ΔV_(LE), will increaseby the same percentage. Consequently, the PHDs shown in FIG. 7 for aparticular set of particle diameters will shift upward in pulse heightvalue by the same percentage.

We will now consider the crucial task of converting the “raw” data—thePHD—obtained from a sample of suspended particles into the objectultimately desired—the particle size distribution, or PSD. It is usefulto compare this task conceptually with the operation required in thecase of a conventional LE- or LS-type sensor. There, the height of thepulse due to passage of a particle through the OSZ is nearly independentof its trajectory, because the intensity of the incident beam isdesigned to be approximately constant across the flow channel (i.e.along the x-axis) for a given z-axis value (e.g. z=0). Consequently,particles of a given size ideally give rise to pulses of substantiallythe same height, and the resulting PHD is therefore, in effect,equivalent to the final desired PSD. There is a one-to-onecorrespondence between a given, measured pulse height, ΔV_(LE) (orΔV_(LS)), and the particle diameter, d. If particles of a larger orsmaller size pass through the sensor, the resulting pulse heights arelarger or smaller, respectively. A “calibration curve,” consisting ofpulse height vs particle diameter, is all that is needed to obtain, bysimple interpolation, the PSD from the PHD. Obtaining the raw PHD datausing the conventional SPOS method is equivalent to determining thefinal, desired PSD.

By contrast, as discussed earlier, the response of the new LE- (or LS-)type sensor is much more “convoluted.” Even in the simplest case ofparticles of a single size, the resulting PHD consists of a broadspectrum of pulse heights, from the smallest values just above theprevailing noise fluctuations, to the maximum value, ^(M)ΔV_(LE) (or^(M)ΔV_(LS)), associated with that size. Therefore, in the typical caseof particles of widely varying size, the resulting PHD consists of aneven wider assortment of pulse heights. No longer is there a simplecorrespondence between pulse height and particle size. It is thereforeno longer a simple, straightforward procedure to transform the set ofparticle counts vs pulse-height values contained in the PHD into thedesired size distribution—particle counts vs particle diameter.

Conversion of the PHD to the desired PSD requires three distinctprocedures. First, the raw PHD must be inverted, or deconvoluted, usinga specialized mathematical algorithm. Its purpose is to convert the“wide-spectrum” PHD produced by the new LE- (or LS-) type sensor into a“sharp”, idealized PHD, equivalent, in effect, to what would have beenobtained using a conventional LE- (or LS-) type sensor. Such anidealized, deconvoluted PHD—hereinafter referred to as the DPHD—has theproperty that all pulses of a given height, ΔV_(LE) (or ΔV_(LS)), belongexclusively to particles of a given size (assuming, always, particles ofa given composition). The dPHD is equivalent to what would have beenobtained if all of the particles contributing to the original PHD hadpassed through the center (axis) of the incident beam.

A second straightforward procedure is then carried out. A preliminary,or “raw”, PSD is obtained from the dPHD by simple interpolation of thecalibration curve that applies to the specific new LE- (or LS-) typesensor utilized—e.g. the curve shown in FIG. 8A. This procedure permitsa one-to-one translation of each deconvoluted pulse height value in theDPHD into a unique particle diameter associated with this value, thusyielding the raw PSD. A third procedure is then needed to convert theraw PSD thus obtained into a final PSD that is quantitatively accurate.The number of particle counts in each diameter channel of the raw PSD isthe number of this size that actually contributed to the measured PHD.As discussed above, this is typically only a small fraction of the totalnumber of particles of the same size (i.e. within the size range definedby the diameter channel) residing in the volume of sample suspensionthat passed through the sensor during data collection. This fraction,φ_(d), of particles actually detected by the new LE- (or LS-) typesensor varies significantly with the particle diameter, d, as shown inFIG. 9. Therefore, in the third and final procedure, the number ofparticles contained in each diameter channel of the raw PSD must bemultiplied by the value of 1/φ_(d) that applies for that channel. Thisoperation yields the final, desired PSD, describing the number ofparticles of each size estimated to reside in the quantity of samplesuspension that passed through the sensor during data acquisition.Values of 1/φ_(d) for each value of diameter, d, can be obtained fromthe sensor efficiency curve, φ_(d) vs d, by interpolation.

There are two independent algorithms presented herein for deconvolutinga measured PHD, to obtain the dPHD, hereinafter referred to as “matrixinversion” and “successive subtraction.” Implementation of eitherprocedure is based on the property that the response of the new LE- (orLS-) type sensor—like its conventional SPOS counterpart—is additive.Because the particles passing through the sensor give rise to signalpulses one at a time, the resulting PHD can be considered to be composedof a linear combination, or weighted sum, of individual PHDscorresponding to uniform particles of various sizes, referred to as“basis vectors.” (This term is well known in linear algebra.) Each ofthese basis vectors represents the response of the system to astatistically significant number of particles of a single, given size.Examples include the PHD shown in FIG. 4, obtained for d=1.588-μm, andthe eight PHDs shown in FIG. 7.

The measured PHD can be referred to as PHD(ΔV), where ΔV denotes thepulse height, ΔV_(LE) or Δ_(VL)S, depending on the type of new sensoremployed. It is considered to be constructed from a linear combinationof N basis vectors, referred to as PHD_(I)(ΔV), where I=1,2. . . ,N.PHD₁(ΔV) is the vector for d=d₁; PHD₂(ΔV) is the vector for d=d₂; . . .and PHD_(N)(ΔV) is the vector for d=d_(N). Therefore, PHD(ΔV) can bewritten asPHD(ΔV)=c ₁ PHD ₁(ΔV)+c ₂ PHD ₂(ΔV)+ . . . +c _(N) PHD _(N)(ΔV)  (9)

The weighting coefficients, c₁, c₂, . . . c_(N), constitute the desiredsolution to Equation 9. These coefficients represent the values in eachof the dPHD channels.

The eight measured PHDs shown in FIG. 7 constitute basis vectors thatcan be used for the deconvolution of any measured PHD. However, clearlythere are too few of these vectors to permit computation of a dPHD ofacceptable pulse height resolution, and therefore a PSD ofcorrespondingly acceptable size resolution. Typically, one must use amuch larger number of basis vectors, much more closely spaced (in pulseheight), in order to achieve reasonable resolution in the final PSD. Theprospect of obtaining a relatively large number of basis vectors (e.g.32, 64 or 128) by measuring a similarly large number of samples ofuniform particles, appropriately spaced, is impractical (if notimpossible, given the lack of a sufficient variety of commerciallyavailable particle size standards).

However, according to the invention, the required large number of basisvectors can be obtained by one or more straightforward procedures,starting with a relatively small number of vectors generatedexperimentally (like the eight shown in FIG. 7). As discussed earlier, aPHD having a desired maximum pulse height value, ^(M)ΔV_(LE) (or^(M)ΔV_(LS)), can be obtained from an existing (e.g. experimentallydetermined) PHD, having a smaller maximum pulse height value, by“stretching” the latter along the pulse height axis. The pulse-heightvalue for each channel of the existing PHD is multiplied by a factorequal to the ratio of the “target” value of ^(M)ΔV_(LE) (or MΔVLS) tothe lower value. Conversely, a PHD having a higher maximum pulse heightvalue than the “target” value can be “compressed” downward as desired,using for the multiplicative factor the ratio (smaller than unity) ofthe lower to the higher maximum pulse-height values. In principle,therefore, an arbitrarily large number of basis vectors can be obtainedfrom a small starting set of (measured) basis vectors, using thesestretching or compressing operations. Instead of determining the smallnumber of basis vectors experimentally, they may also be computed from asimple theoretical model. The remaining column basis vectors can then becomputed by interpolation and/or extrapolation from these “computed”basis vectors. It is also possible to compute all of the required basisvectors from the theoretical model.

Two algorithms have been utilized to solve Equation 9. The conventional,well-known method, called matrix inversion, is summarized schematicallyby the flow diagram shown in FIG. 13A. There are two startingquantities, PHD and M. Quantity PHD, written in bold type, is a 1 x Ncolumn vector, containing the “source” data. The first (i.e. top) columnvalue is the number of particles in the first channel of the measuredPHD. The second column value is the number of particles in the secondchannel of the measured PHD, and so forth. Finally, the Nth (i.e.bottom) column value is the number of particles in the Nth (last)channel of the measured PHD. Parameter N, equal to the number ofpulse-height channels (and corresponding particle-diameter channels ofthe raw PSD), is chosen according to the desired resolution of the PSD.Typical values are 32, 64 and 128. Quantity M is a square (N×N) matrixcontaining the N basis vectors, each of which is a separate 1×N columnvector. Hence, the first column of M contains PHD_(I)(ΔV); the secondcolumn contains PHD₂(ΔV); . . . and the Nth column contains PHD_(N)(ΔV).

The solution of Equation 9 is well known from linear algebra,c=M ⁻ *PHD  (10)where M⁻¹ is a matrix which is the inverse of matrix M. Multiplicationof M⁻¹ by the source vector, PHD, yields the desired result, the 1×Ncolumn vector, c, constituting the desired dPHD vector. The individualcontents (values) for each of the N channels must be multiplied by anappropriate factor, so that the sum of the contents, c₁+C₂+ . . .+c_(N), is the same as the total number of particles that contributed tothe measured PHD in the first place, thus ensuring conservation of thetotal number of particles.

A second method, called successive subtraction, has been developed forsolving Equation 9. This represents a novel and powerful technique fordeconvoluting the measured PHD. In the case of the new LE- (or LS-) typesensor, the successive subtraction method provides a particularlyeffective and useful procedure for deconvoluting the PHD. As discussedabove, what is so unusual about the response of the LE- (or LS-) typesensor is the shape of the PHD obtained for uniform-size particles.Specifically, it is highly asymmetric, possessing a sharp cut-off and,hence, a well-defined maximum pulse height value, ^(M)ΔV_(LE) (orMΔVLs). From the point of view of the deconvolution process, this is animportant and useful property. The channel of the PHD that has thelargest pulse height value (assuming that it contains a statisticallysignificant number of particle counts) identifies the largest particlesize that can be present in the PSD (apart from over-size outliers).This is the diameter, d_(I), of the basis vector having a maximum pulseheight value that coincides with the maximum pulse height found in themeasured PHD.

The successive subtraction algorithm is conceptually simple. Thecontribution of the maximum-size basis vector, PHD_(I)(ΔV), with anappropriate weighting, or scaling, factor (reflecting the number ofparticles of that size that contributed to the original PSD) issubtracted from the starting PHD. This leaves an “intermediate” PHDvector that has a smaller total number of particle counts and a smallerremaining maximum pulse height value. This operation is then repeatedsuccessively using the remaining basis vectors corresponding tosmaller-size particles, until the entire starting PHD effectively“disappears,” or is substantially “consumed,” leaving virtually noremaining particle counts or channels to be accounted for.

The successive subtraction algorithm is described schematically by theflow diagram shown in FIG. 13B. The starting measured PHD column vectoris duplicated as an intermediate column vector, b. In addition, columnvector c, that ultimately will become the solution (dPHD), isinitialized to zero (i.e. a 1×N column vector of all zeros). As before,the N×N square matrix M contains the N basis vectors that have beenselected to perform the deconvolution. Two calculation “loops” are thenutilized: I=N, N−1, 1 and, within the I-loop, J=N, N−1, . . . , 1. Inthe larger I-loop, starting with I=N, the Ith column of matrix M ismultiplied by the Ith element of vector b. This becomes a new I×N columnvector, called a. The Ith element in vector c is then set equal to theIth element of vector b, and vector a is subtracted from vector b.

Next, the calculation enters the secondary J-loop. Starting with J=N, adecision is made based on the value of the Jth element in vector b. Ifit is less than zero, the Jth element is set equal to zero. In eithercase, the J-loop cycles back to the beginning, and this query isrepeated for J=N−1, continuing in the same fashion all the way to J=1.After the J-loop is completed, the computation returns to the beginningof the I-loop. The operations within the I-loop are then repeated forI=N−1. These include calculation of vector a, equating of the Ithelement of vector c with the Ith element of vector b, and subtraction ofvector a from vector b. After all cycles of the I-loop have beencompleted, one obtains vector c—the desired dPHD.

FIG. 14 contains a schematic diagram that summarizes the operationalstructure of the LE- (or LS-) type sensors and methods of the invention,including all measurement and computational steps needed to obtain thefinal desired PSD. A sensor 100 of the LE-type incorporating theprinciples of the present invention as described with respect to thesensor of FIG. 3 responds to a relatively concentrated particlesuspension to produce output V_(LE). It will be observed that outputV_(LE) has a voltage baseline level V₀ ^(T) that is lower than baselinevoltage V₀ in the absence of turbidity. This reduction in the voltage iscaused by turbidity introduced by a relatively concentrated suspensionbeing fed through sensor 100. Turbidity correction is introduced at 102,resulting in an overall signal V¹ _(LE), raising the baseline voltagelevel to V₀. The d.c. component of the signal is effectively removedfrom V_(LE) ¹ by subtraction (or a.c. coupling) in 104, and the signalis also inverted at 104 to produce pulse height signal ΔV_(LE).Alternatively, a sensor 106 of the LS-type that also incorporates theprinciples of the present invention may provide a pulse height signalΔ_(VL)S. A pulse height analyzer 108 organizes the pulse height signalΔV (ΔV_(LE) or ΔVLS) into a pulse height distribution PHD, as shown inFIG. 15A. A deconvolution calculation using matrix inversion orsuccessive subtraction is performed at 110 to produce a deconvolutedPHD, dPHD. The deconvolution calculation requires a matrix M that isconstructed at 112 with column basis vectors that correspond toparticular particle diameters. These, as explained below, will either bemeasured at 113 by sending particles of known size through the sensor(either LE or LS) or computed at 114.

The dPHD, as shown in FIG. 19A, is converted to “raw” PSD (particle sizedistribution) at 116 through the use of calibration curve 118 whichplots the relationship between pulse height ^(M)ΔV against particlediameter as shown in FIG. 8A. The raw PSD is then converted at 120 tothe final PSD result. The raw PSD is normalized by multiplying by 1/Φdfrom sensor efficiency curve 122, as shown in FIG. 9, and adjusted by avolume factor from an analysis of sample volume at 124.

In order to obtain PSD results having the highest possiblereproducibility and resolution, it is necessary to optimize thequality—specifically, signal/noise ratio and reproducibility—of themeasured PHDs from which the PSDs are obtained by deconvolution.Therefore, as has already been pointed out, a statistically significantnumber of particles of each relevant size (i.e., each small range ofrelevant sizes) must pass through the OSZ of the new sensor and bedetected. However, there is another, equally critical factor thatinfluences the quality of the PHD (and subsequent PSD) results. Thisinvolves the spatial distribution of particle trajectories with respectto the illuminating beam, as discussed below.

It is useful to review the PHD obtained for uniform (1.588-μm)polystyrene latex spheres, shown in FIG. 4. Clearly, this PHD possessesa high dynamic range—i.e., a high ratio of the particle counts obtainedfor (approximately) the highest pulse-height channel (≈5600) to thenumber measured for the lowest channel (≈100). This high ratio is aconsequence of the fact that the flow of fluid and particles through theflow channel of the new sensor has been designed so as to yield asubstantially uniform distribution of particle trajectories across thewidth (x-axis) of the channel. All distances, |x|, of closest approachof the trajectories to the axis of the light beam are sampled withapproximately equal probability. In particular, therefore, particleswill pass through the central portion of the beam (i.e., withtrajectories close to A in FIG. 5), giving rise to the largest number ofcounts at substantially the maximum pulse-height value. Particles willalso pass with equal probability through all lesser intensity regions,yielding successively fewer counts at successively smaller pulse-heightvalues.

If the flow of particles is distorted in such a way as to causenon-uniform sampling of |x| values, then the shape of the resulting PHDobtained for uniform particles will be different from that shown in FIG.4. Specifically, in an inferior apparatus (e.g., having poor fluidicsdesign), the trajectories might be clustered in such a way as to causethe particles to avoid the central, high intensity region of the beam.In this case, the high-count peak portion of the PHD will effectively betruncated, resulting in a much lower ratio of maximum to minimum counts.

If there is significant spatial non-uniformity in the distribution ofparticle trajectories, then this non-ideal distribution must bemaintained for all PHD measurements. The basis vectors, whether measuredor computed, must relate to the same non-uniform distribution oftrajectories as that which occurs during measurement of an unknownsample. Otherwise, there will be significant distortion of the DPHD andcorresponding PSD. In practice, it may be difficult, if not impossible,to maintain a particular, non-uniform spatial distribution of particletrajectories over an extended period of time, given the number ofvariables that come into play. Hence, in practice it is necessary todesign the flow channel and associated fluidics system, as well as theillumination/detection optics, in such a way as to produce a spatialdistribution of trajectories that is substantially uniform.

It is instructive to test the effectiveness of the deconvolutionprocedure for converting the measured PHD to the raw PSD, using a samplethat has a simple, known size distribution. FIGS. 15A, B, C show thePHDs obtained using the new LE-type sensor for a series of threemixtures of uniform polystyrene latex “standard” particles (DukeScientific, Palo Alto, Calif.), each containing three sizes: 0.993-μm,1.361-μm and 1.588-μm. Each of the PHDs was obtained by passing 16-ml ofthe particle suspension through the sensor at a flow rate F=20 ml/min,resulting in a data collection time of 48 sec. These PHDs wereconstructed using 64 channels, evenly spaced on a logarithmic scale ofΔV_(LE), from 5 mV to 5000 mV. The choices of 64 channels and 16-mlsample volume resulted in acceptably low statistical fluctuations in thenumber of collected particle counts in each channel, yielding stable,reproducible dPHD results following deconvolution and very good sizeresolution in the resulting PSD, as seen below.

The sample used in FIG. 15A consisted of 0.5-μm of prediluted 0.993-μmlatex stock, plus 1-ml of prediluted 1.361-μm latex stock, plus 2-ml ofprediluted 1.588-μm latex stock. In all cases the original latex stocksuspensions consisted of 1% (w/w) solids (density ρ=1.05), and thepredilution factor was 1000:1. The sample used in FIG. 15B was the sameas that used for 15A, except only one-half the amount of 0.993-μm latexstock was used (0.25-ml, instead of 0.5-ml). The sample used in FIG. 15Cwas the same as that used for 15B, except the amount of 0.993-μm latexstock was again reduced by a factor of two (0.125-ml, instead of0.25-ml). The total number of particle counts contained in the threePHDs was 102,911 (A), 90,709 (B) and 81,827(C).

There are important qualitative features of the PHDs shown in FIGS. 15A,B, C that are immediately evident. First, as expected, there is a widerange of ΔV_(LE) values present in each PHD, with the characteristic“left-decaying” shape (i.e. falling from high to low ΔV_(LE) values)seen previously for uniform-size particles (e.g. in FIGS. 4, 6 and 7).Notwithstanding the wide range of pulse heights obtained, the trimodalnature of the underlying PSDs is clearly evident for each of the threesamples. Second, there is the characteristic, abrupt “cut-off” in eachPHD that defines its upper end—i.e. the maximum pulse height value,^(M)ΔV_(LE), for the entire distribution, as seen in the PHDs obtainedfor uniform-size particles. For all three samples the value of ^(M)ΔVLE(i.e. at the midpoint of the highest channel) is 326 mV. (This ignoresthe existence of small numbers of particle counts at larger pulseheights, due to over-size particles and possibly coincidences, asdiscussed previously.)

The effectiveness of the deconvolution procedures described above can beverified by applying them to the measured PHDs shown in FIGS. 15A, B, C.It is instructive to compare the dPHD results obtained from the twoproposed deconvolution algorithms using the same data. First, it isuseful to show an example of the matrix that can be used to deconvolvethe measured PHD vectors using either technique. For convenience indisplaying the numerous entries contained in the matrix and vectors, itis useful to employ a reduced channel resolution of 32, rather than thevalue of 64 adopted for the PHDs shown in FIGS. 15A, B, C. Anappropriate 32×32 matrix is therefore shown in FIGS. 16A and 16B, inwhich all entries have been rounded to three decimal places for ease ofdisplay.

Each of the rows of the matrix corresponds to successive pulse heightchannels with increasing row numbers indicating increasing pulse heightsignals. As discussed above, each column of the matrix represents abasis vector corresponding to a particular size. Nine of these vectorswere obtained experimentally, by measuring the PHDs for a series ofuniform polystyrene latex particles, as discussed earlier. Each measuredbasis vector was assigned to that column of the matrix for which themaximum count value lies on the diagonal—i.e. where the row and columnnumbers are the same. In the 32×32 representation shown in FIGS. 16A and16B, the measured basis vectors (associated with the diametersindicated) occupy columns #6 (0.722-μm), #8 (0.806-μm), #12 (0.993-μm),#17 (1.361-μm), #19 (1.588-μm), #20 (2.013-μm), #26 (5.03-μm), #29(10.15-μm) and #31 (20-μm). The entries for each column basis vectorhave been renormalized, so that the peak value equals unity in eachcase. The remaining 23 empty columns in the matrix are then filled upwith “theoretical” basis vectors, where each entry is obtained by linearinterpolation or extrapolation of the corresponding entries in nearbymeasured vectors, equivalent to the “stretching” operation discussedearlier.

The source data column vectors representing the measured, 32-channelPHDs for the three different samples are shown in FIG. 17. (The contentsof adjacent pairs of channels in the PHDs shown in FIGS. 15A, B, C wereadded together to obtain the necessary 32-channel values.) The resultsobtained by deconvolution of the PHDs, using the method of matrixinversion (FIG. 13A), are also shown in FIG. 17 for the three respectivesamples. Each of the resulting dPHDs clearly confirms (even in thistabular format) the trimodal nature of each distribution, showingrelatively “clean” separation of the three latex size standards (giventhe limitations on resolution imposed by the use of 32 channels). The“smearing” of pulse heights across a wide spectrum seen in the originalPHDs due to the dependence of sensor response on particle trajectory hasbeen successfully “removed” by the straightforward matrix inversionprocedure, with no assumptions made concerning the shape of theunderlying PSD.

Several details are noteworthy. First, dPHD results of relatively highquality—i.e. containing few (and only low-amplitude) spurious “noise”contributions, as shown in FIG. 17, can be consistently obtained usingthe new SPOS method by “cleaning up” the matrix used to invert themeasured PHD data. This consists of setting equal to zero the secondaryentries (most of which typically are relatively small to begin with)that lie below the unit elements on the diagonal. These terms correspondto counts for pulse height values greater than the maximum count pulseheight value in the column. Second, each of the dPHDs generated by thematrix inversion algorithm typically contains several negative valuesfor various channels (bins). These non-physical values are arbitrarilyset equal to zero, for obvious reasons. The entries in the remainingchannels are then renormalized, so that the total number of particlesequals the total number of counts originally collected in thecorresponding measured PHD. Third, the pulse height values associatedwith the three main peaks (i.e. the channels having the three largestnumber of particles) observed for the dPHDs in FIG. 17 are the same forall three samples—65 mV (Row 12), 198 mV (Row 17) and 309 mV (Row 19).Interpolation of the calibration curve of FIG. 8A yields thecorresponding particle diameters—0.94 μm, 1.31 μm and 1.55 μm. Thesevalues should be considered to be in good agreement with the knownsizes, given the limited resolution associated with the 32 channelschosen for the matrix inversion calculation. Finally, the expectedprogressive, factor-of-two decrease in the number of 0.993-μm particles(Row 12) in going from sample A to B to C is indeed observed, at leastapproximately (discussed below).

Next, it is useful to compare these results with the dPHDs obtained fromthe same starting PHD data using the novel method of successivesubtraction, with the same 32-channel resolution. The matrix andmeasured PHD column vectors are the same as those used for matrixinversion. The resulting dPHDs obtained using the successive subtractionalgorithm are also shown in FIG. 17. Clearly, there is very goodagreement, from channel to channel (i.e. row to row in the dPHD columnvectors), between the values generated by the two differentdeconvolution procedures. Specifically, there is substantial agreementfor the channels associated with the three expected latex peaks,encompassing rows 11-3 and 16-22. The only deviations concern theoccasional spurious entries of low amplitude, most prevalent in lowerpulse-height channels (i.e. rows # 1-10). They occur because ofinadequacies in the inversion algorithms, given inevitable statisticalnoise in the underlying PHD data. More of these contributions appear tobe generated by the matrix inversion method than by the successivesubtraction algorithm. This should not be surprising, given theadditional “information” possessed by the latter method and the factthat the dPHD thus produced evolves systematically, from largest tosmallest pulse-height channels. In any case, apart from the small noisecontributions noted above, one can conclude that the dPHD resultsproduced by the two deconvolution procedures are: 1) very good,concerning both absolute accuracy (i.e. particle diameters correspondingto pulse-height values) and resolution; and 2) substantially the same.

These conclusions are reinforced by the dPHD results obtained from thesame PHD data using higher, 64-channel resolution. The starting PHDs nowconsist of 64×1 column vectors, corresponding to the 64-channel datashown in FIGS. 15A, B, C. The matrix is a 64×64 array, having four timesthe number of entries as the matrix shown in FIGS. 16A and 16B. Again,nine measured basis vectors were used as a starting point forconstructing the 64×64 matrix. The new 64×1 (column) vectors wereobtained from the same measured PHDs that produced the 32×1 basisvectors used in the preceding analysis. The new vectors occupy columns#11 (0.722-μm), #15 (0.806-μm), #24 (0.993-μm), #34 (1.361-μm), #37(1.588-μm), #41 (2.013-μm), #51 (5.03-μm), #58 (10.15-μm) and #61(20.0-μm).

The resulting 64-channel dPHDs obtained by matrix inversion are shown inFIGS. 18A, B, C. The corresponding results obtained by successivesubtraction are shown in FIGS. 19A, B, C. Again, the agreement betweenthe two sets of results is excellent, comparable to the agreementobserved using 32-channel resolution, summarized in FIG. 17. As before,the three peaks are cleanly separated, but with the advantage of havingtwice the pulse-height resolution. There remain some minor “noise”contributions observed in the lower pulse-height region of the matrixinversion results (FIGS. 18A, B, C), whereas there are almost noartifacts observed for the 64-channel successive subtraction results(FIGS. 19A, B, C). Hence, one can again conclude that the dPHD resultsobtained using the successive subtraction algorithm are marginallybetter than those obtained by simple matrix inversion.

Only two, straightforward computational procedures remain in order toconvert the dPHD results (from either deconvolution algorithm) into thedesired final PSD results. First, the DPHD must be transformed into a“raw” PSD, using the standard calibration curve that applies for thesensor utilized—i.e. the plot shown in FIG. 8A. Second, the resultingraw PSD must be renormalized, taking into account the relatively lowsensor efficiency, φ_(d), for all particle sizes measured. The number ofparticles contained in each channel of the raw PSD must therefore bemultiplied by the factor 1/φ_(d) that pertains to the diameter, d, forthat channel, where φ_(d) is obtained from FIG. 9 by interpolation. Theresulting renormalized values represent the number of particles of eachsize estimated to have been in the volume of sample suspension thatpassed through the sensor during data collection. Dividing these numbersby the sample volume (16-ml for the trimodal latex samples discussedabove) yields the concentration of particles of each size estimated tobe in the sample suspension. The resulting “concentration” PSDs,corresponding to the dPHDs obtained by successive subtraction (FIGS.19A, B and C) and expressed as the number of particles per ml of samplesuspension (divided by 1000), are shown in FIGS. 20A, B, C.

It is instructive to compare the particle concentrations found in eachpopulation peak in the three PSDs obtained using the new LE-type sensorwith estimates obtained independently. The concentrations of theindividual stock latex suspensions used to prepare samples A, B and Cwere measured using a conventional (combined LE+LS) SPOS instrument with100% counting efficiency. Much higher dilution factors were required inorder to avoid distortions in the measured PSDs caused by coincidenceeffects. These comparisons are summarized in Table II. The contributionsof the individual histogram bars belonging to each of the three “peaks”in the concentration PSDs of FIGS. 20A, B, C were added together toobtain the concentrations shown for each latex standard size.

Clearly, the agreements are very good, considering the limitationsinherent in any deconvolution procedure that would be employed,including the two methods discussed herein. Of course, neither theresolution nor the absolute accuracy of the PSDs obtained using the newLE-type sensor can be expected to be quite as good as what would beobtained using a conventional sensor. Nevertheless, the quality of theresults obtained using the new LE-type sensor should be consideredexcellent, given the radically different optical design utilized and therelatively sophisticated deconvolution methods required. Finally, it isimportant to acknowledge that the PSD results shown in FIGS. 20A, B, Care greatly superior to the typical results that would be produced byany “ensemble” technique, in which particles of all sizes contributesimultaneously to the measured signal. The latter must then be inverted,using an appropriate algorithm, to obtain an estimated PSD, usuallyhaving relatively limited resolution and accuracy. Such ensembletechniques include ultrasonic attentuation as a function of frequencyand, notably, “laser diffraction,” based on a combination of classicalMie scattering and Fraunhofer diffraction.

Next, it is instructive to examine the response of the new LE-typesensor for a sample suspension containing a continuous (“smooth”),relatively broad distribution of particle diameters. Specifically, it isuseful to focus on a colloidal suspension that is “mostly submicron,” inwhich the great majority of particles, even on a volume-weighted basis,are smaller than one micron (1 μm). There are many applications of bothcommercial and research significance that involve the use of suchcolloidal suspensions. Examples include: 1) aqueous “slurries” ofultrafine inorganic particles—usually oxides, such as silica, aluminaand cerium oxide—used for CMP processing of silicon wafer surfacesduring fabrication of semiconductor integrated circuits; 2) homogenizedoil-in-water emulsions designed for intravenous injection, used forparenteral nutrition, drug delivery (e.g. anesthesia) and as contrastagents for ultrasound imaging; 3) inks, dyes and pigments, used for bothink-jet and conventional printing; 4) homogenized artificial drinkemulsions, consisting of edible oil droplets, containing flavor andcoloring agents, coated with an emulsifier and suspended in water; 5)aqueous paper coating dispersions, typically containing calciumcarbonate, kaolin clay, titanium dioxide or organic polymers, such aslatex; 6) polymer suspensions, used in paints, coatings and adhesives.

For these and other applications it is often very useful to be able todetermine the number and size distribution of the largest particles inthe sample suspension—i.e. those that comprise the outermost “tail” ofthe PSD, e.g. larger than ≈1 μm. Knowledge of the volume, or mass,fraction of the particles in the PSD tail (i.e. percentage of the totalparticle volume, or mass) often provides a clear indication of thequality and/or stability of the emulsion, suspension or dispersion inquestion. If the material is colloidally unstable, the volume fractionof particles occupying the PSD tail will “grow” over time, as the systemmoves toward irreversible agglomeration and/or phase separation.Characterization of the entire PSD, typically requiring an “ensemble”technique, such as laser diffraction or dynamic light scattering, bynature usually lacks the sensitivity needed to detect small changes inthe PSD associated with the early stages of particle/dropletagglomeration. Instead, the SPOS technique is able to detectquantitatively very small changes in the PSD associated with variousstages of instability, because it responds only to the relatively largeparticles that comprise the outermost tail of the PSD. This tail mayconstitute only a very small fraction (typically<0.1%) of the particlesthat populate the overall PSD, even on a volume-weighted basis. However,this small fraction of the PSD frequently provides a unique “window” onthe stability of the overall suspension.

The same can be said regarding the power of the SPOS technique to revealthe quality of a suspension or dispersion. SPOS methods have proven tobe very useful, if not essential, for determining the quality of manyparticle-based products, even when long-term stability is not inquestion. The quality of such products or intermediate process materialsis often correlated strongly with the percentage of particles thatpopulate the outlier region of the PSD tail. Their presence must oftenbe minimized, or excluded altogether, in order to ensure product qualityand performance. The number- or volume-weighted PSD obtained for thetail can therefore be used to optimize the parameters that control theparticle manufacturing process. Examples of the latter includehomogenization and Microfluidization™ (Microfluidics Corp., Newton,Mass.) for preparation of oil/water emulsions, where the pressure,temperature, orifice size, stoichiometry of constituents, the number ofpasses and other variables influence the PSD. Other examples includeemulsion polymerization (using batch, semi-batch or continuous reactors)for production of polymers, and milling and grinding of powders. Thesuperiority of the conventional LE-type SPOS method compared to laserdiffraction for determining the stability and quality of injectable fatemulsions is described by D. F. Driscoll et al, in Int'l J. Pharm., vol.219, pp. 21-37 (2001).

The new LE-type sensing method offers two potentially significantadvantages over its conventional counterpart. First, much less dilutionof the starting concentrated suspension is required. This feature isoften very important—i.e. for systems that may become colloidallyunstable, and therefore susceptible to agglomeration, due to theextensive dilution usually required by conventional LE or LS sensors inorder to avoid particle coincidences. An important example includes CMPslurries, stabilized by electrical charges on the particle surfaces,maintained by the relatively high or low pH of the surrounding fluid.Significant (e.g. 100- or 1000-fold) dilution of these slurries canchange the pH sufficiently to significantly decrease the electricalpotential on the particles, allowing Van der Waals attractive forcesbetween neighboring particles to overcome electrostatic repulsions, thuspromoting agglomeration.

Second, the new LE-type SPOS method can usually achieve an acceptablelow size threshold (e.g. <0.7 μm) without needing to resort to aseparate LS measurement—i.e. using light extinction alone. The resultingLE-type signal is relatively insensitive to deterioration of the innersurfaces of the flow channel due to absorbance (coating) of particles orchemically induced damage (e.g. etching) caused by the suspending fluid.While these effects can significantly degrade the performance of anLS-type sensor, due to strong scattering at the fluid-surfaceinterfaces, they usually have relatively little effect on the quality ofthe LE signal, except in extreme cases. Therefore, the requirements formaintenance (cleaning) of the flow cell can be expected to be relativelymodest over extended times for most important applications.

With these considerations in mind, it is useful to review some typicalresults that can be achieved by the new LE-type sensor for a typical,relatively concentrated colloidal suspension. FIGS. 21A, B, C to 23A, B,C summarize the results obtained for three samples containing injectable(oil-in-water) fat emulsion, used for parenteral nutrition. Each samplecontained a fat droplet concentration of approximately 0.05% (byvolume), obtained from a 400:1 dilution of the “stock” lipid emulsion(Liposyn m, 20% (w/v), Abbott Laboratories, N. Chicago, Ill.). This isequivalent to a droplet volume fraction of 5×10⁻⁴ ml per ml of finalsuspension. Sample “A” contained only fat droplets, while “B” and “C”contained added amounts of uniform 0.993-μm polystyrene latexparticles—3.25×10⁵ particles/ml for “B” and 8.13×10⁴ particles/ml for“C.” Expressed in terms of volume fraction, the added latex “spikes” areequivalent to 1.67×10⁻⁷ ml per ml of suspension for “B” and 4.17×10⁻⁸ mlper ml of suspension for “C.” Compared to the volume fraction of fatdroplets, the added latex spike concentrations are equivalent to 334 ppm(parts per million) and 84 ppm, respectively.

FIGS. 21A, B, C show the measured PHDs obtained for the three respectivesamples, using 32 pulse height channels, evenly spaced on a logarithmicscale. In each case data were collected from a sample volume of 16 ml,at a flow rate of 20 ml/min, over a 48-sec period. For pulse heightsabove approximately 14 mV, the PHD for sample A shows a smoothlydecreasing number of detected particles with increasing pulse height.This is not surprising, given the fact (confirmed below) that theunderlying PSD should have a similarly decaying population withincreasing droplet size for droplets larger than the mean size of thedistribution, approximately 0.2 μm. The fact that the PHDs decreasebelow 14 mV is a consequence of the fact that particles with maximumpulse heights, ^(M)ΔV_(LE), smaller than this value are too small to bedetected individually (i.e. below approximately 0.7 μm) for the sensorutilized. The sensor efficiency falls off precipitously below thislevel. The PHD for sample B clearly shows the perturbation due to theadded latex spike. The same is true for the PHD generated by sample C,with a considerably smaller effect due to the 4×reduction in added latexparticles.

FIGS. 22A, B, C show the dPHDs obtained by deconvolution of the PHDs ofFIGS. 21A, B, C, respectively, using the successive subtractionalgorithm. The dPHDs exhibit the expected decaying behavior, mimickingthe expected underlying size distribution of fat droplets. The addedlatex spike is now more clearly recognizable in FIG. 22B and, to alesser extent, in FIG. 22C. The dPHDs are shown only for^(M)ΔV_(LE)≧21.3 mV, because below this value the distribution isdistorted and unreliable due to failing detection and resolution, aswell as particle coincidence. These effects give rise to the “rollover”in the measured PHDs seen in FIGS. 21A, B, C, alluded to above.

The resulting PSDs for the three samples, expressed in terms of particleconcentration in the original suspensions, are shown in FIGS. 23A, B, C.They were obtained from the corresponding dPHDs of FIGS. 22A, B, C usingthe calibration curve in FIG. 8A and the sensor efficiency curve in FIG.9, as discussed earlier. The vertical concentration axis has beengreatly expanded, to provide a clearer view of the details of thedistributions. The influence of the added latex spikes is clearly seenin FIGS. 23B and C.

It is instructive to compare quantitatively the measured vs expectedeffects of each latex spike. The known concentration of added latex wasapproximately 2.33×10⁵ particles/ml for sample B and 5.83×10⁴/ml for C.The corresponding measured values are estimated by subtracting the PSDobtained for sample A from the PSDs found for samples B and C,respectively. Most of the contributions to the PSDs due to the addedlatex can be accounted for by considering the four histogram bars from0.90 to 1.06 microns, inclusive. The resulting enhanced particleconcentration for sample B is 3.01×10⁵/ml, compared to the actual addedvalue of 3.25×10⁵/ml. The corresponding values for sample C are8.85×10⁴/ml (measured) vs 8.13×10⁴/ml (known). Both sets of valuesshould be considered to be in very good agreement, given the relativelysmall concentrations of added latex particles and the inherentlydemanding nature of the deconvolution procedure and related calculationsrequired to obtain the final PSDs.

The histogram plots discussed above are representative of the resultsthat can be obtained routinely using the new LE method for thelarge-particle tail of the PSD for a wide variety of colloidalsuspensions and dispersions. Often it is necessary, or simplyconvenient, to dilute the starting concentrated sample as little aspossible, for the reasons mentioned earlier. Hence, in many cases thesuspension passing through the flow cell is relatively highlyconcentrated, and therefore necessarily very turbid. Therefore, theintensity of the light transmitted through the turbid sample, over thethickness, b, of the flow channel is significantly reduced, relative towhat it would be for a relatively transparent sample.

There are two consequences for the resulting LE signal, VLE. First, the“baseline” d.c. level, V₀, in the absence of a particle (in the OSZ)sufficiently large to create a detectable pulse, will decrease. The newbaseline voltage level, called V^(T) ₀, is ideally related to the levelin the absence of turbidity, V₀, by Beer's Law,V ^(T) ₀ =V ₀ exp(−αx)  (11)where x is the distance through which the light beam traverses thesample (i.e. x=b), and α is the coefficient of absorbance, orattenuation, usually expressed in units of cm⁻¹. Equation 11 can beexpected to be accurate provided the sample is not excessively turbid,such that it would no longer exhibit idealized attenuation vs distancebehavior, due to strong multiple scattering.

The second consequence of sample turbidity is that the (negative-going)pulses resulting from detectable particles passing through the OSZ arealso diminished in height (voltage). The resulting measured pulseheight, ΔV^(T)LE, for a given particle will decrease with respect to itsvalue in the absence of turbidity, ΔV_(LE), by the same proportion thatV^(T) ₀ is decreased with respect to V₀, assuming moderate turbidity anda linear system response. Therefore, if no corrections are made to theset of pulse heights, the resulting PHD will be shifted systematicallyto lower pulse height values. The same will be true for the resultingdPHD, obtained by deconvolution of the PHD. Hence, the resulting PSDwill be shifted to smaller particle diameters—i.e. all of the particlesin the sample will be systematically undersized.

There are several methods that can be used to address the problem ofshrinkage in pulse heights resulting from sample turbidity, typicallycaused by the large population of ultra-fine particles lying below thesize detection threshold—i.e. too small to contribute directly to thePHD. In the first, simplest approach, each measured pulse height can be“renormalized” (either in real time or after data collection) to its“ideal” value, ΔV_(LE), in the absence of turbidity, which is related tothe measured pulse height, ΔV^(T)LE, byΔV _(LE)=(V ₀ /V ^(T) ₀)×ΔV ^(T) LE  (12)The scale factor by which all of the measured pulse heights must bemultiplied in order to obtain a new set of idealized pulse heights,corresponding to negligible turbidity, is V₀/V^(T) ₀. The baselinevoltage level in the absence of sample turbidity, V₀, can be easilymeasured by passing fluid substantially devoid of particles through thesensor. This value can be stored for future use whenever a turbid sampleis to be analyzed, or it can be re-measured prior to each new sampleanalysis, using clean fluid. The baseline level in the presence ofturbidity, V^(T) ₀, can be measured by passing a portion of the samplesuspension through the sensor, prior to data collection.

There are at least two ways in which V^(T) ₀ can be determined. Theeasiest, analog approach consists of measuring the time-average value ofthe overall signal, V_(LE)(t), over an appropriate period (e.g. 1 sec),using a passive or active filter, having an appropriate (RC) timeconstant. The average value can be measured using either a stationary ora flowing suspension. In the latter case the discrete pulses due todetectable particles will influence the measured average value. However,the extent of the influence will usually be relatively small, given thatthe average pulse rate is typically less than 10,000/sec and the pulsewidths are usually shorter than 10-12 μsec, resulting in a “duty cycle”for the pulses of less than 10%. A second approach to measuring V^(T) ₀consists of digitizing (using an analog-to-digital converter) asignificant segment (e.g. 10-100 msec) of the entire signal, V_(LE)(t),when the turbid sample is flowing through the sensor, and analyzing theresulting digitized signal, prior to collecting pulse height data forthe sample. A computer, suitably programmed, can be used to identify andmeasure the “flat” (apart from small fluctuations due to noise) portionsof the signal lying on either side of the discrete pulses, correspondingto the desired baseline level, V^(T) ₀.

FIG. 26A is a block diagram of one embodiment of means for compensationfor turbidity by renormalizing the pulse heights to the value expectedin the absence of turbidity. The sensor has a light source 126 andfocusing lens 127 directing a beam of light 128 through a measuring flowchannel 130 illuminating an optical sensing zone 131 within measurementflow channel 130. A fluid suspension of particles 132 flows throughmeasurement flow channel 130 and a small fraction of particles 132flowing through measurement flow channel 130 flow through opticalsensing zone 131. When particles 132 pass through optical sensing zone131, light is blocked and this is detected by a LE photodetector D_(LE)as pulses 134 extending downwardly from baseline voltage V₀ ^(T). Itwill be observed that baseline voltage V₀ ^(T) and pulses 134 are bothsmaller than baseline voltage V₀ and pulses 135 which would be providedif the fluid suspension was not turbid. A converter 136 converts thecurrent signal I_(LE)(t) generated by photodectector V_(LE) in responseto the passage of particles 132 to a voltage signal V_(LE)(t).

In order to compute a correction factor G, a non-turbid liquid is passedthrough the system, and the baseline voltage V₀ is measured at 138.Then, the specimen to be measured is passed through the system and thebaseline voltage V₀ ^(T) is measured at 140. The ratio G=V₀/V₀ ^(T) isthen calculated at 142.

The signal V_(LE)(t) developed by converter 136 is processed to subtractthe d.c. portion through the use of a.c. coupling and is inverted at144. The output ΔV_(LE) ^(T) (t) is then amplified by adjustable gainamplifier 146, the gain of which is controlled by correction factor G.The corrected signal ΔV_(LE) (t) as seen in plot 148 contains properlysized pulses with proper pulse heights 150.

FIGS. 24A, B, C and 25A, B, C summarize the typical results obtained fora turbid sample before and after renormalization, respectively, of themeasured pulse heights, using the first method described above. Thesample consisted of a “double-spiked” suspension of relativelyconcentrated fat droplets, obtained from the same stock emulsionemployed earlier. The fat droplet concentration was approximately 0.5%(by volume)—i.e. ten times larger than what was used for the previouslydiscussed measurements. The resulting suspension was highly turbid froma visual point of view. Two “spikes” of uniform latex particles—2.013-μmand 10.15-μm—were added to the turbid sample suspension. Theconcentrations of added latex particles were large enough to yield anadequate, statistically stable number of counts during data collection,but small enough to have negligible effect on the overall turbidity ofthe suspension.

FIG. 24A shows the measured PHD (64 channels) obtained for the mixtureof concentrated fat droplets and added latex particles. FIG. 24B showsthe resulting dPHD obtained from the PHD by deconvolution (successivesubtraction). The resulting raw PSD, before correction for sensorefficiency, is shown in FIG. 24C. Clearly, the two peaks associated withthe latex spikes are shifted to substantially lower diameters than thevalues that would be obtained for a bimodal latex mixture alone, in theabsence of concentrated fat droplets. The mean diameters displayed forthe two peaks are approximately 1.5-μm and 6.5-μm.

The average baseline level, V^(T) ₀, measured for this turbid sample was3.45 volts—a significant decrease from the normal value of 5.00 volts,obtained in the absence of turbidity. It should therefore be possible torecover accurate PSD results by renormalizing the original PHD, using ascale factor of 5.00/3.45, or 1.45, and repeating the deconvolutioncalculations. The renormalized PHD is shown in FIG. 25A, and theresulting dPHD obtained by deconvolution (successive subtraction) isshown in FIG. 25B. The corresponding raw PSD is shown in FIG. 25C. Thelocations of the two peaks associated with the latex spikes,approximately 1.9-μm and 9.8-μm, are now very close to the expectedvalues.

There is a second method that can be used to accommodate samples thatare significantly turbid. The signal processing system can be designedto be adjusted automatically in order to substantially eliminate theeffects of turbidity at the outset—i.e. before pulse height data arecollected. The starting, depressed baseline level, V^(T) ₀, can beincreased by appropriate signal-conditioning means, so that itapproximates the value, V₀ that would have been obtained in the absenceof turbidity. For example, an amplifier means with adjustable,voltage-controlled gain can be used. A feedback circuit means can beused to sense the conditioned output signal amplitude and increase thegain of the amplifier means until the output baseline voltage reachesthe desired, “ideal” level, V₀. This second method is illustrated in theembodiment of FIG. 26B. As before, converter 136 provides signalV_(LE)(t). In this case, the signal is amplified by adjustable gainamplifier 152, the gain of which is controlled by correction factor G.The amplified signal Gx V_(LE)(t) is adjusted so that the baseline levelis equal to the “ideal” level V₀. The signal is now processed with thed.c. component subtracted and with the pulses inverted at 154, againproducing the output shown in plot 148 with properly sized pulses withproper pulse heights 150.

Alternatively, the computer that is used to control the particle-sizinginstrument can be used (in conjunction with a digital-to-analogconverter) to control the gain of the amplifier means, so that thedesired baseline level, V₀, is reached. In another scheme, an analogmultiplier means can be used to multiply the uncorrected startingsignal, V_(LE)(t), by a second voltage, effectively equal to V₀/V^(T) ₀,where the value of V^(T) ₀ is obtained from the time average ofV_(LE)(t), before or during data collection.

Each of these electronic schemes for raising V^(T) ₀ up to V₀effectively constitutes an automatic gain control, or AGC, system, thatcompensates either once (before data collection) or continuously (duringdata collection) for changes in the baseline level due to changes insample turbidity. Then, data can be collected and analyzed using thedesired deconvolution algorithm and related procedures, as discussedabove. The resulting PHD will be substantially accurate, without theshifts to lower diameters that would otherwise result from theturbidity. (This conclusion assumes that the turbidity is not excessive,resulting in nonlinear response.)

There is a third method, related to the second one discussed above,that, in principle, can be used to restore the baseline level to thevalue that it would have in the absence of turbidity. Rather thanincreasing the output signal using an amplifier means with an adjustablegain, the intensity of the light source means can be increased by thesame desired factor, V₀/V^(T) ₀. This method assumes that the lightsource means is normally operating at less than half of its availableoutput power, allowing for increases of ×2, or greater, as needed. Thismethod is shown in FIG. 26C in which the intensity of the light beamprovided by light source 126 is controlled by control factor G. Theoutput signal V_(LE)(t) from converter 136 is then directly connected tobe processed at 156 where the d.c. component is subtracted and thepulses are inverted. The output pulses 150 are again properly sized.

The second method of restoring the baseline level to V₀ before datacollection was utilized for the measurements of the 0.05% fat emulsionsamples (plain and spiked), summarized in FIGS. 21A, B, C through 23A,B, C. The uncorrected measured baseline level, V^(T) ₀, was 4.82 volts,compared to V₀=5.00 volts without turbidity. From Equation 11 and x=0.02cm, one obtains α=1.83 cm⁻¹. In the case of the 0.5% fat emulsion sampleshown in FIGS. 24A, B, C and 25A, B, C, the measured value of 3.45 voltsfor V^(T) ₀ implies α=18.55 cm⁻¹, which should theoretically be 10×larger than the value of a obtained for the 10× less concentratedsample. Indeed, there is close agreement. The small discrepancy may beascribed to experimental error or departure from Beer's Law due to theonset of multiple scattering.

FIGS. 27A, B, C and 28A, B, C summarize the results (32-channelresolution) obtained using the new LE-type sensor for another colloidalsuspension—an aqueous slurry of silica, 12.5% (vol.) concentration, usedfor CMP processing. Each sample was measured without dilution, madepossible because the refractive index of the silica is relatively closeto the value for water. Even though the resulting turbidity was stillsignificant, it was nevertheless much lower than the typical valuesobtained for suspensions of the same concentration containing particlesmuch less matched in refractive index to the surrounding liquid.

The measured PHD for the fully concentrated silica CMP slurry is shownin FIG. 27A. The resulting dPHD (obtained by successive subtractiondeconvolution) in the reliable pulse-height range is shown in FIG. 27B(expanded y-axis). The resulting PSD, expressed as the particleconcentration in the original sample suspension, is shown in FIG. 27C.The y-axis is expanded 20-fold to accentuate the relatively lowconcentration of particles that populate the PSD tail.

The same starting silica slurry was then spiked with a very lowconcentration of 0.993-μm latex particles—1.30×10⁵/ml. The measured PHDis shown in FIG. 28A and the resulting dPHD is shown in FIG. 28B, wherethe effect of the latex perturbation is clearly evident. The finalconcentration PSD is shown in FIG. 28C. The added latex particles areeasily detected. This is an impressive accomplishment for the newLE-type sensor, given the fact that this added latex spike representsonly approximately 0.5 ppm of the total particle volume. Hence, thismethod possesses more than enough sensitivity to permit reliable,quantitative detection of outlier particle populations in silica-baseCMP slurries caused by a variety of physical and chemical stressfactors. Such increases in potentially damaging over-size particles arefrequently correlated with increases in defects on wafer surfaces duringCMP processing, resulting in lower yields of usable integrated circuitdevices. The ability to monitor the “health” of potentially unstable CMPslurries during processing, with sensitivity to very small changes inthe concentration of problematic particles, with little or no dilutionrequired, represents a significant advance in CMP slurry metrology.TABLE I Particle Diameter Dilution/Concentration Counts/16-ml MaximumPulse Ht, ^(M)ΔV_(LE) 0.806 μm (“A”) 800,000:1 of 10% (wt) 37,870  33 mV(0.66% of 5V) 0.993 μm (“B”) 40,000:1 of 1% (wt) 73,377  81 mV (1.62%)1.361 μm (“C”) 20,000:1 of 1% (wt) 56,815  221 mV (4.42%) 1.588 μm (“D”)10,000:1 of 1% (wt) 83,702  326 mV (6.52%) 2.013 μm (“E”) 2,000:1 of0.45% (wt) 83,481  482 mV (9.64%) 5.030 μm (“F”) 100:1 of 0.3% (wt)97,983 1552 mV (31.0%) 10.15 μm (“G”) 40:1 of 0.2% (wt) 31,423 3385 mV(67.7%) 20.00 μm (“H”) 20:1 of 0.3% (wt) 14,833 4473 mV (89.5%)

TABLE II Latex Concentration (# Particles/ml) - Computed PSD vs ExpectedValues (*) 0.993-μm Peak 1.361-μm Peak 1.588-μm Peak Sample PSD ExpectedPSD Expected PSD Expected A 318 325 165 177 242 272 B 168 163 190 177252 272 C 67 81 187 177 272 272

A first preferred embodiment of the invention, shown schematically inFIG. 29, incorporates both the new LE- and LS-type SPOS sensors of theinvention in a single sensor, having two independent output signals,V_(LE) and V_(LS). The resulting dual “LE+LS” design offers increasedcapability and flexibility, providing single-particle counting andsizing over a relatively large range of particle sizes. The LS-typesensor subsystem can be used to extend the size range below the lowerdetection limit provided by the new LE-type sensor subsystem. The extentto which the lower particle size limit can be extended depends on avariety of parameters. These include: the width, 2w, of the narrow(typically focused) beam within the measurement flow cell; the power ofthe light source; the range of angles over which scattered light iscollected for implementation of the new LS-type sensing function; andthe physical properties, including the refractive index, of both theparticles and the suspending fluid.

The new dual LE+LS sensor includes a light source 160, preferablyconsisting of a laser diode module, typically having an outputwavelength in the range of 600 to 1100 nanometers (nm). The beam 162produced by the light source means preferably is collimated (parallel)and “circularized”—i.e. the intensity is a function only of thedistance, r, from the central axis. Furthermore, the beam preferably hasa gaussian intensity profile, as described by Equation 7, along any axisnormal to the axis of propagation of the beam. The new LE+LS sensor alsoincludes a focusing means 164, typically a single- or multi-elementlens, capable of focusing the starting collimated light beam 162 to thedesired beam width, 2w, at the center of the measurement flow channel166 in the OSZ 168, consistent with the desired particle size range. Itis assumed that the focusing means has an appropriate focal length, thusyielding acceptable values for both the width and depth of field of thefocused beam. The latter is preferably significantly longer than thethickness, b, of the flow channel, in order to optimize the resolutionof the resulting PSD.

The measurement flow cell 166 is fabricated from a suitable transparentmaterial, such as glass, quartz or sapphire, or alternativesemi-transparent material, such as PTFE (e.g. Teflon™, manufactured byDuPont) or other suitable plastic that is sufficiently transparent atthe operating wavelength and compatible with the fluid-particle mixture.A suitable fluidics system, including a flow pump means and optionalmeans for automatic dilution of the starting sample suspension (ifneeded), are typically required to facilitate the steady flow of theparticle-fluid suspension through flow cell 166. The flow rate, F, isusually chosen to be the same as, or close to, the value used togenerate the calibration curve for the LE- or LS-type sensor.

The thickness, b, of the flow channel should be small enough to achievea high coincidence concentration limit and as uniform a beam width aspossible (ideally with b<<depth of field), resulting in improvedresolution for the final PSD. However, it must be large enough toprevent frequent clogging by over-size particles (e.g. agglomeratedprimaries and contaminants in the fluid/diluent). The width, a, of theflow channel is also chosen to strike a compromise between two competingeffects. A relatively large value reduces the impedance to the flowingfluid-particle mixture and lowers the velocity (and increases the pulsewidth) for a given flow rate, F. However, the larger parameter a, thesmaller the sensor efficiency, φ_(d), for any given particle diameter,d. This results in a smaller fraction of particles in the sampleactually contributing to the measured PHD and final PSD, which, if toosmall, may be undesirable.

The new LE+LS sensor contains two separate light collection anddetection subsystems, used independently to extract the desired LE- andLS-type signals. The LE-type signal can be captured using a small lightreflecting means M (e.g. mirror), positioned so as to intercept thenarrow beam 167 of incident light after it passes through the flow celland fluid-particle mixture. The resulting transmitted beam 169, thusdeflected away from the optical axis of the combined sensor, is causedto impinge on a nearby light detection means V_(LE). The lattertypically consists of a small-area, solid-state (silicon) detector,operating in a linear region and having a spectral response that ismatched to the wavelength of light source 160, thus providing an outputsignal with an acceptable signal/noise (S/N) ratio. The output of thedetector means is typically a current (the “photocurrent”), which can beconditioned by a current-to-voltage converter (“transimpedance”amplifier) 170, yielding an output signal in the generally desired formof a time-varying voltage, V_(LE)(t), shown schematically in FIG. 2.

Alternatively, a small detector element can be placed directly in thepath of the light beam 167 after it emerges from the flow cell, thuseliminating the need for the intermediate light reflecting meansdiscussed above. Regardless of whether a mirror or detector element isused to “capture” the transmitted light beam, there are tworequirements. First, the means used must function as an effective beam“stop.” That is, it must be able to prevent any significant fraction ofthe arriving light flux from being reflected back toward the flow cell,thus becoming a source of “stray” light. Through unintended internalreflections from the various optical surfaces, a portion of the straylight can find its way to the scattering detection means D_(LS), thuscorrupting the resulting LS signal, by contributing a portion of theincident intensity to the latter. Second, the means used to capture theLE signal must be small enough not to intercept, and therefore block,scattered light rays at any angles that are intended to be captured andredirected to the light detection means D_(LS), as discussed below.

Separately, scattered light originating from particles passing throughOSZ 168 is collected over a range of scattering angles, θ, with θ₁≦θ≦θ₂,where angles θ₁ and θ₂ are defined by a suitable aperture means, such asan annular mask 172 fabricated from a photographic negative with anouter opaque portion 174, a transparent intermediate portion 176, and aninner opaque portion 178. The scattered rays selected by mask 172 areallowed to impinge on a collecting lens 180 of appropriate focal lengthand location, which converts the diverging scattered rays into anapproximately parallel beam 182. A second lens 184 is then typicallyused to refocus the rays onto a relatively small light detection meansD_(LS). As in the case of the LE subsystem, the output signal of D_(LS)is typically a current, which can be optionally conditioned, typicallyby means of a transimpedance amplifier 186, so that the final output isin the form of a time-varying voltage, V_(LS)(t), shown schematically inFIG. 12.

The signals V_(LE)(t) and V_(LS)(t) are organized into respective pulseheight distributions PHD by pulse height analyzers 188 and 189. The PHDsare then respectively deconvoluted in computer deconvolution means 190and 191, which ultimately compute a pair of respective particle sizedistributions PSD 192 and 193.

As should be obvious, this embodiment can be implemented as an LE-typeor LS-type sensor only, simply by removing (or not installing in thefirst place) the optical elements, detection means and signalconditioning circuitry associated with the unwanted subsystem. In thiscase, it may be useful to adjust the width, 2w, of the focused beamwithin the measurement flow channel, in order to optimize the resultingperformance of the LE- or LS-type sensor. This parameter will impact theusable particle size range, coincidence concentration limit and minimumdetectable particle size differently for the two sensing modes, asdiscussed earlier.

A second embodiment is shown schematically in FIG. 30. For greatestcapability and flexibility it also incorporates both LE- and LS-typesubsystems. However, as in the case of the first embodiment, only thosecomponents that are needed for one or the other subsystem need beprovided, if desired. The main difference between this embodiment andthe embodiment of FIG. 29 concerns the use of optical fibers to conveylight from a remote light source 194 into the sensor and to transmit thecaptured LE and LS light “signals” from the sensor to remote lightdetection means, similarly located outside the sensor. The mainattribute of this design is the absence of electronic components orassociated circuitry physically within the sensor proper. Consequently,a sensor based on this design requires no electrical power at the siteof the sensor and is, by definition, immune to electrical interference,including stray electromagnetic radiation, which may exist in theimmediate vicinity of use.

As shown in FIG. 30, an optical fiber 190 is used to carry light from anexternal light source 194 to within the sensor housing. It is useful,although not necessary, to use a single-mode (rather than a multi-mode)optical fiber for this purpose. When used in conjunction with a remotelaser diode light source 194 (which, together with a suitable lens 198,launches light into the input end of fiber 190), this type of fiber actsusefully as an optical “spatial filter,” or waveguide. By being able tosupport only a single mode of optical radiation, this fiber delivers aspatially “clean,” circular beam 199 at its output end, having thedesired gaussian intensity profile. Through the use of simpleoptics—e.g. two focusing lenses 200 and 201, as shown in FIG. 30—thediverging conical light beam is ultimately focused within measurementflow channel 166 into a narrow beam 202 with the desired final width,2w, as discussed above.

Optical fiber 204 is used to capture the focused light beam transmittedthrough the flow cell, conveying it to light detection means D_(LE),connected to signal conditioning circuitry 206, both of which arelocated outside the sensor. Optical fiber 208 is used to capturescattered light rays originating from OSZ 168 over a range of scatteringangles, optionally using optical elements similar to those used toimplement the LS subsystem in the first embodiment, including mask 172with opaque portions 174 and 178, transparent portion 176, and lenses180 and 184. The captured scattered light is conveyed to separate lightdetection means DLS, connected to signal conditioning means 210, both ofwhich are also located outside the sensor. Optical fibers 204 and 208are typically chosen to be multimodal. The property of spatial filteringthat is usefully provided by a single-mode fiber, such as fiber 190, forlight input is typically not useful for light collection. Multimodalfibers are available with much larger cores, thus making it easier tocapture all of the light rays of interest, thereby facilitating theoptical alignment of both the LE and LS detection subsystems. Thesignals V_(LE)(t) and V_(LS)(t) provided by signal conditioning means206 and 210 are analyzed at PHAs 188 and 189 and deconvoluted at 190 and191 to provide respective PSDs.

As indicated, the embodiment of FIG. 30 yields a sensor that iselectrically passive. Consequently, this design is potentially usefulfor particle sizing applications in challenging environments, oftenencountered in “online” process monitoring. One such example involvesexplosive environments. A sensor based on the embodiment of FIG. 30would eliminate the need for a cumbersome and expensive explosion-proofenclosure (including an inert gas purging system) at the point ofuse/installation of the sensor. Another example is an environmentcontaining high levels of electromagnetic radiation or electricalpower-line noise, resulting in susceptibility of electronic circuitry toinduced noise. Through the use of this embodiment of FIG. 30, the lightsource and detection means can be located in a remote area, where theelectrical environment is quieter and the need for electrical shieldingless demanding.

Another advantage of this embodiment is reduced complexity, andtherefore cost. This may constitute a significant advantage inapplications that require numerous sensors at different locations, whereease of replacement and service may be an important consideration. Apartfrom the possible need to replace a flow cell, because of damage to theinner surfaces due to particle contamination (coating) and/orsolvent-related etching, there is no other component that would requirereplacing. Rather, the unpredictable, time-consuming and costly serviceassociated with replacement of laser diode sources and repair ofelectronic circuitry (associated with the light detection means) wouldbe performed at a central location. Environmental challenges at thepoint of use of the sensors, including temperature and humidityextremes, hazardous/explosive atmospheres and difficulty of access, canpresumably be reduced or avoided altogether by performing most sensorservice functions at a centralized, optimized location.

A third embodiment, shown schematically in FIG. 31, incorporates twovariations of the LE-type sensing apparatus of the invention within thesame physical sensor. This new “dual LE-type” sensor includes thefamiliar light source 160—typically the same kind of laser diode moduleutilized in the embodiment of FIG. 29, producing a collimated, circularbeam 162 with a gaussian intensity profile. (Alternatively, the startinglight beam can be delivered by optical fiber from an outside lightsource means, as envisioned in the embodiment of FIG. 30.) This lightbeam is divided into two beams 212 and 213 of approximately equalintensity, by a beam splitter means 214. (An intensity ratio rangingfrom 50/50 to 60/40, or even 70/30, is typically acceptable.)

The portion of the original light beam passing through beam splitter 214is reduced in width at 216 to the desired value, 2w₁, at the center ofmeasurement flow channel 166. It passes through a first OSZ 219 using anappropriate focusing means 218, which is typically a single- ormulti-element lens, similar to the means used in the embodiment of FIG.29. After this beam passes through the flow cell, it is caused toimpinge on a light detection means D_(LE1), typically consisting of asmall silicon photodiode. The resulting photocurrent signal isconditioned at 220, typically using a transimpedance amplifier, so as toyield the desired time-varying LE-type signal, V_(LE1)(t).(Alternatively, an optical fiber can be used to capture the transmittedlight flux and deliver it to a remote light detection means, asenvisioned in the second embodiment.) Signal V_(LE1)(t) is analyzed at222 to form the PHD and deconvoluted at 224, ultimately to form thedesired PSD.

As discussed above in connection with FIGS. 8A and 10, for any givenbeam width there is a range of particle diameters over which there isacceptable sensitivity in the response—i.e. a significant change in themaximum pulse height, ^(M)ΔV_(LE), with a small change in particlediameter, d. For a beam width of 10-11 μm, discussed extensively above,acceptable sensitivity and resolution are obtained over the approximatesize range of 1 to 20 μm—i.e. from one-tenth to twice the beam width, or(0.1-2)×(2w₁).

Therefore, it is useful to provide a second LE-type measurement withinthe same sensor, for which the low-size end of its effective sizingrange begins approximately where the high-size end of the first new LEsubsystem terminates—e.g. 20 μm, using the example above. This can beaccomplished if the beam width, 2w₂, established in the flow channel bythe second LE-type subsystem obeys the approximate relationship,2×(2w₁)>0.1×(2w₂), or (2w₂)≈20×(2w₁). Using the example above, thisimplies a width of 200 μm for the second focused beam, yielding aneffective size range for the second LE-type subsystem of approximately20 to 400 μm.

The second LE-type subsystem is easily implemented, as indicated in FIG.31. The portion 213 of the original light beam deflected by beamsplitter 214 is redirected toward the flow cell using a mirror 226,appropriately oriented. Beam 213 is reduced in width to the desiredvalue, 2w₂, within the flow channel using an appropriate focusing means228. The focal length and location of the latter will obviously bedifferent than the corresponding parameters required for focusing beam212. Alternatively, beam 213 may be passed directly through the flowchannel without the use of a focusing means, provided that its width isalready close to the desired value for the second LE-type subsystem. Thesecond beam 213 is directed through a second OSZ 232 in measurement flowchannel 166 to a second photo detector D_(LE2). The signal isconditioned at 234 to provide signal V_(LE2)(t) which is analyzed at236, forming the PHD, which, in turn, is deconvoluted at 238, ultimatelyto produce the desired PSD.

The inset plot 230 in FIG. 31 shows schematically the relationshipbetween the sensor responses for the two LE-type subsystems—i.e.^(M)ΔV_(LE1) vs d and ^(M)ΔV_(LE2) vs d. Using the example discussedabove, a wide range of particle diameters can be analyzed by this dualLE-type subsystem—a conservative estimate is 1 to 400 μm.

The signals produced by the two new LE-type subsystems are independentof each other. In general, the PHDs produced by each subsystem will havebeen generated by completely different particles. Provided that each PHDcontains a statistically significant number of particle counts (i.e. ineach pulse height channel), it is unimportant whether any or all of theparticles detected by one subsystem are also detected by the othersubsystem during an analysis measurement. If the axes of the two beamsare perfectly “lined up” (i.e. have the same x-axis value), then all ofthe particles that pass through the OSZ defined by the first beam shouldalso pass through the OSZ defined by the second beam, given that it islarger. In practice it may be necessary to collect data in twointervals—first, at a relatively high concentration for the smaller,first beam, and then again at a lower concentration for the larger,second beam, to avoid coincidence effects.

A fourth embodiment is shown schematically in FIG. 32A. In addition toan optical LE-type sensor, it consists of a LS-type sensor of theinvention that includes a means for selecting different ranges of anglesover which scattered light is collected and directed onto a detectionmeans D_(LS) to obtain the desired LS signal, V_(LS)(t). As discussedabove, the scattered intensity is a strong function not only of theparticle size, but also of the refractive indices of both the particleand the surrounding fluid. Proper selection of the range of anglespermits the total intensity signal to be maximized, while avoiding“reversals” (non-monotonic behavior) in the response curve of integratedintensity vs particle diameter. Therefore, optimization of the sensorperformance often requires a different angular range for eachapplication (particle type) of interest.

As shown, the desired angular range is selected by rotating a wheelcontaining several different aperture masks 241, 242, 243, and 244. Eachmask is designed to permit transmission of only those scattered raysthat lie within the desired angular range, allowing them to reach thelight-gathering lens. The wheel is rotated into one of severalappropriate positions, each of which assures proper alignment of thedesired mask—i.e. with its center on the optical axis defined by theincident beam and lenses. The wheel can be rotated manually to thedesired position and then locked in place. Alternatively, a miniaturemotor 246 (e.g. stepper-type) and gear and belt system 248 can be usedto position the desired mask automatically, by means of an electricalsignal from the central control system of the sensor.

FIG. 32B shows an elevation view with the four masks 241-244 shown moreclearly. The inset in FIG. 32B indicates four possible types of angularranges that might be used, defined by the minimum and maximum angles ofacceptance, θ₁ and θ₂, respectively. Mask 241 selects a narrow range ofsmall angles—i.e. both θ₁ and θ₂ relatively small. Mask 242 selects awide range of angles—i.e. θ₁ small and θ₂ relatively large. Mask 243selects a narrow range of relatively large angles—i.e. θ₁ relativelylarge and θ₂ only moderately larger. Mask 244 selects a wide range ofrelatively large angles—i.e. θ₁ relatively large and θ₂ substantiallylarger.

The other components shown in FIG. 32A are identical to the likenumbered parts in the embodiment of FIG. 29.

In a variation of this embodiment, the rotating wheel in FIG. 32A can bereplaced by a thin, rectangular-shaped plate, or card, fabricated frommetal or plastic, that contains a single aperture mask. Insertion of thecard into a properly located slot in the side of the sensor housing thenbrings the aperture mask into correct alignment between the flow celland collecting lens. The desired angular range for measuring aparticular sample can be selected by inserting the particular cardcontaining the appropriate aperture mask for that sample. Thecalibration curve corresponding to the selected angular range is thenused to obtain the PSD, following processing of the raw PHD data, asdiscussed above.

Alternatively, in another variation of this embodiment, the rotatingwheel in FIG. 32B can be replaced by a single, adjustable annulus,consisting of an adjustable outer opaque iris, surrounding an adjustableinner opaque iris, having the same central axis. The annular regionbetween the inner and outer opaque irises is transparent, allowingscattered light rays originating from the OSZ in the flow channel toreach the light collecting lens(es) and, ultimately, the LS detectormeans, D_(LS). The range of scattering angles over which the scatteredlight rays are collected and contribute to the LS signal are defined bythe inner and outer circumferences of the adjustable, transparentannulus. In one version of this, the annular region of acceptance can beadjusted using a mechanical device—e.g. two independently adjustablemechanical irises, similar to those used in cameras. In another versionof this variation, the adjustable annulus can be realized using anelectro-optical device, such as a two dimensional liquid-crystaldisplay. By applying an appropriate voltage to two sets of contiguous,annular-shaped semi-transparent electrodes, an approximately transparentannular region can be defined between two opaque inner and outerregions. The desired range of scattering angles, θ, where θ_(1≦θ≦θ) ₂,can be chosen by applying voltage to the sets of contiguous annularelectrodes that define the regions which one desires to be opaque—i.e.θ≦θ₁ and θ>θ₂.

A fifth embodiment is shown schematically in FIG. 33. Like the otherembodiments, it may include either the new LE- or LS-type SPOS subsystemof this invention, or both, using a single light source and beamfocusing means to define the OSZ. The distinguishing feature of thesixth embodiment is the use of a light beam with an elliptical gaussianintensity profile, rather than the circular gaussian profile used in theother embodiments. The resulting intensity profile of the focused beamin the flow channel is still described by Equation 7, but where thequantity r²/w² is replaced by (x/p)²+(z/q)², with p>q. Parameters p andq are, respectively, the semi-major and semi-minor axes of theelliptical-shaped imaginary surface of the beam, on which the intensityfalls to (1/e²)×I₀, or 0.135 I₀ where I₀ is the intensity at the centerof the beam (x=z=0). The “aspect” ratio of the resulting ellipticalfocused beam—the extent to which it is elongated—is defined as p/q. Theelliptical beam becomes circular in the limiting case, where p/q=1.

An elliptical beam may be provided with the use of a laser-diode lightsource, which typically provides an elliptical light beam to begin with,before collimation. A beam of this shape may also be provided with acombination of cylindrical lenses or with the use of an aspherical lens.When an elliptical beam with a particular aspect ratio is required, itis possible to use a laser light source in combination with lenses ofthese types or to use such a combination to form a light source with anadjustable aspect ratio. Thus, light source 250 may be a laser lightsource which projects a beam with an appropriate aspect ratio or it mayinclude a combination of cylindrical and/or aspherical lens to providethe required aspect ratio in an elliptical beam 252. A lens 254 thenfocuses the elliptical beam in the OSZ of measurement flow channel 166.Light from the OSZ then is detected by the photodetector D_(LE). Thesignal V_(LE)(t) is then produced by conditioning the output signal at256. This signal is analyzed in PHA 258 to provide the PHD, which isdeconvoluted at 259 to ultimately produce the desired PSD.

As before, the focusing means causes the incident light beam to becomereduced in cross-sectional size within the flow channel. The “width” ofthe resulting focused beam now has meaning only with respect to aparticular chosen axis, normal to the axis of the beam. Whereas a singleparameter, 2w, suffices to describe the width of a circular beam, twoparameters—2p and 2q —are now required to describe an elliptical beam.The aspect ratio of the focused elliptical gaussian beam is the same asthat of the original (collimated) beam before focusing. As shown in FIG.33, the desired orientation of the focused elliptical beam within theflow channel is usually such that the major axis, of width 2p, isperpendicular to the direction of flow of the particles. This axis isalso parallel to the x-axis, along the direction that defines the width,a, of the flow channel (FIG. 3). The minor axis of the focused beam, ofwidth 2q, is parallel to the z-axis and the direction of flow.

There are several significant consequences of the change in beam shape,from circular to elliptical, causing the zone of illumination to extendfurther across the width, a, of the flow cell. First, the resulting OSZalso possesses an elliptical-shaped cross section. A given level ofincident light intensity now extends further from the central axis(x=z=0) of the beam than it would for a circular beam. Therefore, alarger fraction of the particles flowing through the channel will causethe minimum necessary perturbation in the LE (or LS) signal to bedetected, and thereby contribute to the measured PHD. Hence, the sensorefficiency, φ_(d), corresponding to a given particle diameter, d, willincrease relative to the value that would be obtained for a circularbeam of width 2w, having the same total intensity (i.e. light flux),with 2p>2w. At first glance, it might appear that an increase in φ_(d)represents an improvement in the performance of the sensor. However,this “gain” is accompanied by a decrease in the coincidenceconcentration limit of the sensor. If the major goal is maximization ofthe concentration at which the starting sample suspension can bemeasured, without further dilution, then an improvement in φ_(d)achieved at the expense of degradation in the coincidence concentrationprobably results in a net disadvantage. One of the major definingcharacteristics of the new LE- or LS-type sensor of this invention isits ability to obtain relatively accurate and reproducible PSDs,regardless of the fact that only a relatively small fraction of theparticles that pass through the sensor actually contributes to themeasured result. All that is necessary is that a statisticallysignificant number of particle counts are collected in each relevantpulse height channel.

A second consequence of the substitution of an elliptical beam for thenormal circular one is that the sensitivity of the sensor is degraded tosome extent. The cross-sectional area illuminated by the incidentfocused beam and therefore the cross-sectional area of the correspondingOSZ are increased by virtue of the elongation of the beam along thewidth of the flow channel. Thus, the fraction of the illuminated areathat is effectively “blocked,” in the light-extinction sense, by aparticle of a given size is reduced, relative to the fraction blockedfor a circular beam for which 2w=2q, but 2w<2p. Hence, the minimumdetectable particle size threshold for the sensor will be higher than itwould otherwise be for a circular beam.

A third consequence of the elliptical beam, by contrast, isadvantageous. The resulting sensor will possess higher resolution—i.e.in principle the PHD will provide a “cleaner” distinction betweenparticles of nearly the same size. There is now a longer regionextending along the x-axis over which the incident intensity is nearlythe same. This constitutes the “top” of the gaussian profile inintensity, extended in length along the major axis. Therefore, there isa larger set of trajectories, of differing |x| values, for whichparticles are exposed to a similar intensity as they pass through theOSZ. Therefore, the PHD response for uniform particles of a given sizebecomes “sharper.” There is a larger fraction of particle counts in anarrow range of pulse heights immediately adjacent to, and including,the peak of the PHD, with the distribution falling more steeply to lowercount values for pulse heights below the maximum cutoff value. The same,therefore, is true for the various basis vectors that are used fordeconvolution of the PHD, resulting in higher resolution for theresulting dPHD and corresponding PSD. This last characteristicconstitutes the only potential advantage of an elliptical-shaped beam,which may outweigh the accompanying disadvantages, noted above. The usermust determine the net advantage or disadvantage, depending on theapplication.

It is useful to recognize the fact that an elliptical-shaped beamrepresents an intermediate step in the evolution from one “extreme” ofsensor illumination to another. At one end of the sensor-designspectrum, introduced in the current invention, there is a “tight”circular beam of width 2w, yielding the narrowest possible region ofillumination and, consequently, producing the greatest non-uniformity ofresponse. Different particle trajectories give rise to the largest rangeof pulse heights for particles of the same size, as discussedextensively above. There is a major disadvantage associated with thismaximal-nonuniform illumination—i.e. the greatest possible ambiguitybetween pulse height and particle size, requiring the use of adeconvolution procedure to “recover” a reasonably reliable PSD from themeasured PHD.

At the other end of the sensor-design spectrum, there is the traditionalillumination scheme employed by a conventional LE- or LS-type sensor,reviewed earlier (FIG. 1), in which a thin “knife-edge” of incidentlight extends across the flow channel. Ideally, there is very littlevariation in incident intensity along the x-axis (e.g. at maximumintensity, z=0). The variation along the z-axis, for any given x-axisvalue, obeys a gaussian profile. In this other “extreme” case, the pulseheights produced by particles of a given size are ideally the same forall trajectories. Therefore, the measured PHD requires no deconvolutionprocedure, as it effectively is equivalent to the final desired PSD,apart from a calibration factor. This situation represents the mostcomplete tradeoff in sensor characteristics, achieving the highestpossible resolution in exchange for relatively poor sensitivity anddramatically lower coincidence concentration. This illumination scheme,utilized in conventional LE- or LS-type sensors, is conceptuallyachieved by employing an elliptical-shaped beam and “stretching” itsmajor axis, so that p/q approaches infinity in the ideal limit. Itshould be clear that the choice of an elliptical-shaped beam of moderateaspect ratio—e.g. p/q=2 to 4—for use in a new LE- or LS-type sensorresults in a compromise in sensor performance. Somewhat improvedparticle size resolution is obtained, at the expense of somewhat reducedsensitivity and coincidence concentration.

A sixth embodiment of the new LE-type sensor is shown schematically inFIG. 34. A collimated, relatively wide starting beam 261 of lightproduced by a light source 262 is caused to pass through a flow channel166 without the use of a focusing means, as employed in the other sixembodiments. Typically, the effective width of the resultingcylindrical-shaped OSZ would be unacceptably large, yielding relativelypoor sensitivity (i.e. a relatively high minimum diameter threshold) andrelatively low coincidence concentration. A narrower, more acceptableeffective width can be achieved for the OSZ through the use of a novelmeans for limiting the region from which transmitted light rays areallowed to contribute to the LE signal. This objective can be achievedthrough the use of special collimating optics on the “detection side”(as opposed to the light-source side) of the LE-type sensor design shownin FIG. 34.

For example, a specially designed graded-index “GRIN”) collimating lens262, having a very narrow range of acceptance angles and anappropriately small aperture size can be utilized to capture arelatively small fraction of the total light flux transmitted throughthe flow channel. Typically, the output from GRIN collimating lens 262can be conveniently conveyed by optical fiber 264 to a light-detectionmeans V_(LE) connected to appropriate signal conditioning circuitry 266,yielding the desired LE signal, V_(LE), suitable for subsequentprocessing in PHA 268 and deconvolution at 270, as discussed extensivelyabove. GRIN collimating lens 262, depending on its acceptance aperture,ideally captures only those light rays 263 that closely surround thecentral axis of incident beam 261, thus reducing the effective width ofthe resulting OSZ. In effect, GRIN element 262 captures only those raysthat lie at or near the top of the gaussian intensity profile associatedwith incident (transmitted) light beam 261.

The intensity of illumination across the resulting OSZ is thereforerelatively uniform, with a relatively sharp “cutoff” to nearly zeroillumination outside the cylindrical region of acceptance defined byGRIN lens 262. As a result, the sensor efficiency, φ_(d), for a givenparticle diameter, d, will be smaller than it would otherwise be, giventhe relatively wide starting beam. This also results in a highersensitivity to smaller particles and a higher coincidence concentration.In the present case, the OSZ more closely resembles a cylinder ofuniform intensity over its cross section, with a “hard” imaginarysurface, beyond which the intensity drops precipitously to zero. Inprinciple, the resulting PHDs have higher, narrower peaks, becauseparticles that pass through the OSZ give rise to pulses having moresimilar heights. The resulting PSDs therefore have better sizeresolution. An unavoidable disadvantage is relatively poor sizeresolution at the high end of the diameter scale, owing to the sharpercutoff (“hard” outer boundary) of the OSZ. The characteristics andperformance of the resulting sensor, based on the simple scheme shown inFIG. 34, will depend on the detailed design specifications of GRIN lens262.

Although the matrix used in the deconvolution of the PHD is shown withbasis vectors in vertical columns that increase in particle size fromleft to right and rows which extend horizontally across the matrix andincrease in pulse height channel size from top to bottom, the matrixcould be altered in various ways. For example, the column basis vectorscould become row basis vectors, or the increase in particle size for thecolumns could increase from right to left. If row basis vectors areused, the particle size could increase from top to bottom or from bottomto top. Likewise, if pulse height columns are used, the pulse heightchannels could increase from left to right or from right to left. Itshould be observed as well that the column data source vector,containing the measured PHD, could be arranged as a row and/or thedirection of increase could be in one direction or in the reversedirection. It is to be understood therefore that as used in thisspecification and in the claims it is intended that the terms “column”and “row” are interchangeable and that the directions of increase can bereversed.

While the invention has been particularly shown and described withreference to preferred embodiments thereof, it will be understood bythose skilled in the art that the foregoing and other changes in formand detail may be made therein without departing from the spirit andscope of the invention.

1. A method of preparing a matrix for deconvolution of pulse heightdistributions derived from particles of unknown size flowing alongdifferent trajectories through a non-uniform light field of asingle-particle optical sizing device for sizing particles in a fluidsuspension, comprising: determining the value of at least one empiricalbasis vector for said matrix by measuring the response of particles ofknown size flowing through said single-particle optical sizing device;and computing other basis vectors for said matrix corresponding toparticles of other sizes by interpolating and/or extrapolating saidother basis vectors from said empirical basis vector.
 2. A method ofclaim 1, further comprising: determining the value of additionalempirical basis vectors for said matrix by measuring the response ofparticles of known sizes flowing through said single-particle opticalsizing device; and computing said other basis vectors for said matrixcorresponding to particles of other sizes from said at least oneempirical basis vector and said additional empirical basis vectors.
 3. Amethod of preparing a matrix for deconvolution of pulse heightdistributions derived from particles of unknown size flowing alongdifferent trajectories through a non-uniform light field of asingle-particle optical sizing device for sizing particles in a fluidsuspension, comprising: determining the value of at least one computedbasis vector corresponding to particles of at least one size for saidmatrix.
 4. A method of claim 3 further comprising computing other basisvectors for said matrix corresponding to particles of other sizes fromcomputed basis vectors.
 5. A method of deconvoluting a pulse heightdistribution derived from particles of unknown size flowing alongdifferent trajectories through a non-uniform light field of asingle-particle optical sizing device for sizing particles in a fluidsuspension, comprising: setting up a matrix having a plurality ofcolumns, each containing a basis vector comprising a pulse heightdistribution of particles of a known size corresponding to the responseof a photo-detector of said device to said particles of known size, eachsuccessive column containing a basis vector for particles ofsuccessively larger sizes, said matrix also having a like plurality ofrows, each corresponding to a successive pulse height channel, eachchannel including a range of pulse heights, successive rowscorresponding to successively larger pulse heights, each column having amaximum count pulse height value at a location for a row which relatesto a pulse height corresponding to said particle of known sizeassociated with said column, said maximum count pulse height values forsuccessive columns being arranged on a diagonal of said matrix:modifying said matrix by setting all terms corresponding to pulse heightvalues greater than said maximum count pulse height value in a column tozero; and using a deconvolution algorithm to perform matrix inversionand vector multiplication of said pulse height distribution of saidmatrix as modified.
 6. The method of claim 5, wherein, prior to saidmodifying step, renormalizing the values of said basis vectors in saidcolumns by setting said maximum count pulse height value to equal 1.0and all other count pulse height values in said column to a valuemaintaining the same proportionate value to 1.0 that said other countpulse height values had to said maximum count pulse height value of saidcolumn.
 7. The method of claim 5, wherein said response of saidphoto-detection to said particles of known size is developed empiricallyfor some of said basis vectors by sending particles of saidsubstantially known size through said device and providing a response bysaid device to said particles of known size; and computing said responseto said photo-detector for the remaining basis vectors by interpolatingand/or extrapolating said response for said remaining basis vectors fromsaid some of said basis vectors.
 8. The method of claim 5, wherein saidresponse of said photo-detector to said particles of known size iscomputed for some of said basis vectors and said response to saidphoto-detector for the remaining basis vectors is computed byinterpolating and/or extrapolating said response from said some basisvectors.
 9. A method of deconvoluting a pulse height distribution PHDderived from particles of unknown size flowing along differenttrajectories through a non-uniform light field of a single-particleoptical sizing device for sizing particles in a fluid suspension,comprising: setting up a matrix having a plurality of columns, eachcontaining a basis vector comprising a pulse height distribution ofparticles of a substantially known size corresponding to the response ofa photo-detector of said device to said particles of known size, eachsuccessive column containing a basis vector for particles ofsuccessively larger sizes, said matrix also having a like plurality ofrows, each corresponding to a successive pulse height channel, eachchannel including a range of pulse heights, successive rowscorresponding to successively larger pulse heights, each column having amaximum count pulse height value at a location for a row which relatesto a pulse height corresponding to said particle of known sizeassociates with said column, said maximum count pulse height values forsuccessive columns being arranged on a diagonal of said matrix; andimplementing a successive subtraction algorithm comprising the steps of:starting with the basis vector with its maximum count value in thelargest row number; scaling a column basis vector by a factorcorresponding to the value of the row in the PHD that matches the columnnumber; subtracting said scaled basis vector from the PHD to form anelement of a deconvoluted PHD (dPHD), leaving an intermediate PHD vectorwith a smaller number of total particles; and repeating this processusing the remaining basis vectors until the entire PHD has been consumedand all the elements of the deconvoluted dPHD have been formed.
 10. Amethod of compensating a single-particle optical sizing sensor forsizing particles in a relatively concentrated fluid suspension samplefor turbidity of said suspension sample, said sensor operating on alight extinction principle whereby a photo-detector produces signalV_(LE)(t) having a baseline voltage level and a response to blockage oflight by a particle as a downwardly extending pulse from said baselinevoltage level, said method comprising: passing a non-turbid suspensionthrough said sensor; measuring a baseline voltage level V₀ produced inresponse to said non-turbid suspension; passing said relativelyconcentrated suspension sample through said sensor, measuring a baselinevoltage V_(θ) ^(T) produced in response to said relatively concentratedsuspension sample; calculating the ratio${\overset{\_}{G} = \frac{V_{0}}{V_{0}^{T}}};$ and adjusting said sensorin response to G to compensate for said turbidity when said relativelyconcentrated suspension sample passes through said sensor.
 11. Themethod of claim 10, wherein said baseline voltage V₀ ^(T) is effectivelysubtracted from said signal V_(LE) (t), the remaining signal is invertedto produce a pulse height signal ΔV_(LE) ^(T)(t), adjustable gainamplifying means is used to LE amplify said pulse height signal ΔV_(LE)^(T) (t), and said adjustable gain amplifying means is controlled bysaid ratio G to provide a compensated pulse height signal ΔV_(LE) (t).12. The method of claim 10, wherein said signal V_(LE)(t) produced bysaid sensor in response to said relatively concentrated suspensionsample is amplified by adjustable gain amplifier means, the gain ofwhich is controlled by said ratio G to provide a compensated signalV_(LE) (t) having a compensated baseline voltage V₀, subtracting saidbaseline voltage V₀ from said compensated signal V_(LE) (t), andinverting the remaining signal to produce compensated pulse heightsignal ΔV_(LE) (t).
 13. The method of claim 10 wherein saidsingle-particle optical sizing sensor comprises a light source producinga light beam of adjustable intensity, wherein said intensity isincreased in response to said ratio G to compensate for said turbidity.14. A method of optically sizing particles in a fluid suspension,comprising: establishing a flow of said suspension through a physicallywell-defined measurement flow channel of a single-particle opticalsizing sensor apparatus wherein a beam of light, having an axis, isdirected through said measurement flow channel to form an opticalsensing zone within said measurement flow channel, said beam of lightand said optical sensing zone being of such size relative to the size ofsaid measurement flow channel that said sensor apparatus responds toonly a fraction of the total number of particles flowing through saidmeasurement flow channel, whereby said sensor apparatus will respondeffectively to a relatively concentrated fluid suspension, said beamhaving a maximum intensity portion in said beam and a continuum oflesser intensities for positions in said beam spaced transversely fromsaid axis, whereby some of said particles have a trajectory through saidmaximum intensity portion, others of said particles have trajectoriesthrough said lesser intensity positions, and still others of saidparticles may have trajectories outside said zone; detecting light fromsaid zone to provide pulse height signals, each responsive to a particleflowing through said zone, said pulse height signals being functions ofthe sizes and trajectories of detected particles, said pulse heightsignals collectively forming a pulse height distribution PHD; andmathematically deconvoluting and processing said PHD to extract fromsaid PHD a particle size distribution PSD of said particles in saidfluid suspension.
 15. A method of claim 14, wherein said step ofmathematically deconvoluting said PHD comprises determining the value ofat least one empirical basis vector by measuring the response toparticles of known size flowing through said single-particle opticalsizing device; and computing other basis vectors corresponding toparticles of other sizes by interpolating and/or extrapolating saidother basis vectors from said empirical basis vector.
 16. A method ofclaim 15, further comprising determining the value of additionalempirical basis vectors for particles of known sizes flowing throughsaid single-particle optical sizing device; and computing said otherbasis vectors for said matrix corresponding to particles of other sizesby interpolating and/or extrapolating said other basis vectors from atleast one empirical basis vector and said additional empirical basisvectors.
 17. A method of claim 15, further comprising determining thevalue of at least one computed basis vector corresponding to particlesof at least one size.
 18. A method of claim 17, further comprisingcomputing other basis vectors corresponding to particles of other sizesby interpolating and/or extrapolating said other basis vectors fromcomputed basis vectors.
 19. A method of claim 14, wherein said step ofdeconvoluting and processing said PHD comprises setting up a matrixhaving a plurality of columns, each containing a basis vector comprisinga pulse height distribution of particles of a known size correspondingto the response of a photo-detector of said device to said particles ofknown size, each successive column containing a basis vector forparticles of successively larger sizes, said matrix also having a likeplurality of rows, each corresponding to a successive pulse heightchannel, each channel including a range of pulse heights, successiverows corresponding to successively larger pulse heights, each columnhaving a maximum count pulse height value-at a location for a row whichrelates to pulse heights corresponding to said particle of known sizeassociated with said column, said maximum count pulse height values forsuccessive columns being arranged on a diagonal of said matrix;modifying said matrix by setting all terms corresponding to pulse heightvalues greater than said maximum count pulse height value in a column tozero; and using a deconvolution algorithm to perform matrix inversionand vector multiplication of said pulse height distribution and saidinverted matrix as modified.
 20. A method of claim 19, wherein saidresponse of said photo-detector to said particles of known size isdeveloped empirically for some of said basis vectors by directing a flowof particles of said known size through said device and providing aresponse by said device to said particles of known size; and computingsaid response to said photo-detector for the remaining basis vectors byinterpolating and/or extrapolating said response for said remainingbasis vectors from said some of said basis vectors.
 21. As a method ofclaim 14, wherein said step of mathematically deconvoluting said PHDcomprises using a deconvolution algorithm to provide a deconvolutedpulse height distribution dPHD, and said method further comprisingproviding a calibration curve of the relationship of pulse height anddiameter, and using said calibration curve to translate eachdeconvoluted pulse height value in the dPHD into a unique particlediameter associated with this pulse height value yielding a “raw”particle size distribution in PSD, and converting said raw PSD into afinal PSD by renormalizing said raw PSD by multiplying by the value1/Φ_(d), where Φ_(d) is the fraction of particles actually detected bysaid device for particles of each size.